{"id":3653,"date":"2018-12-11T13:57:51","date_gmt":"2018-12-11T18:57:51","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/chapter\/use-radicals-in-functions\/"},"modified":"2018-12-11T13:57:51","modified_gmt":"2018-12-11T18:57:51","slug":"use-radicals-in-functions","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/chapter\/use-radicals-in-functions\/","title":{"raw":"Use Radicals in Functions","rendered":"Use Radicals in Functions"},"content":{"raw":"\n[latexpage]<div class=\"textbox textbox--learning-objectives\"><h3 itemprop=\"educationalUse\">Learning Objectives<\/h3>By the end of this section, you will be able to: <ul><li>Evaluate a radical function<\/li><li>Find the domain of a radical function<\/li><li>Graph radical functions<\/li><\/ul><\/div><div data-type=\"note\" id=\"fs-id1169145658240\" class=\"be-prepared\"><p id=\"fs-id1169147769294\">Before you get started, take this readiness quiz.<\/p><ol id=\"fs-id1169143746917\" type=\"1\"><li>Solve: \\(1-2x\\ge 0.\\)<div data-type=\"newline\"><br><\/div> If you missed this problem, review <a href=\"\/contents\/27141d73-3006-49fa-98eb-5744b312aea7#fs-id1167835419716\" class=\"autogenerated-content\">(Figure)<\/a>.<\/li><li>For \\(f\\left(x\\right)=3x-4,\\) evaluate \\(f\\left(2\\right),f\\left(-1\\right),f\\left(0\\right).\\)<div data-type=\"newline\"><br><\/div> If you missed this problem, review <a href=\"\/contents\/5e548626-8f0f-496d-ab87-4f0358ca2fd3#fs-id1167836521479\" class=\"autogenerated-content\">(Figure)<\/a>.<\/li><li>Graph \\(f\\left(x\\right)=\\sqrt{x}.\\) State the domain and range of the function in interval notation.<div data-type=\"newline\"><br><\/div> If you missed this problem, review <a href=\"\/contents\/da9d6ce0-a078-4ca2-97af-8cb374f040f5#fs-id1167829930477\" class=\"autogenerated-content\">(Figure)<\/a>.<\/li><\/ol><\/div><div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1169145644347\"><h3 data-type=\"title\">Evaluate a Radical Function<\/h3><p id=\"fs-id1169147750184\">In this section we will extend our previous work with functions to include radicals. If a function is defined by a radical expression, we call it a <span data-type=\"term\">radical function<\/span>.<\/p><p id=\"fs-id1169143574637\">The square root function is \\(f\\left(x\\right)=\\sqrt[]{x}.\\)<\/p><p id=\"fs-id1169145658807\">The cube root function is \\(f\\left(x\\right)=\\sqrt[3]{x}.\\)<\/p><div data-type=\"note\" id=\"fs-id1169147959288\"><div data-type=\"title\">Radical Function<\/div><p id=\"fs-id1169145732376\">A <strong data-effect=\"bold\">radical function<\/strong> is a function that is defined by a radical expression.<\/p><\/div><p id=\"fs-id1169145640177\">To evaluate a radical function, we find the value of <em data-effect=\"italics\">f<\/em>(<em data-effect=\"italics\">x<\/em>) for a given value of <em data-effect=\"italics\">x<\/em> just as we did in our previous work with functions.<\/p><div data-type=\"example\" id=\"fs-id1169147834542\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1169148054498\"><div data-type=\"problem\" id=\"fs-id1169147763493\"><p id=\"fs-id1169147767920\">For the function \\(f\\left(x\\right)=\\sqrt{2x-1},\\) find <span class=\"token\">\u24d0<\/span> \\(f\\left(5\\right)\\) <span class=\"token\">\u24d1<\/span> \\(f\\left(-2\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169147759005\"><p id=\"fs-id1169147864033\"><span class=\"token\">\u24d0<\/span><\/p><div data-type=\"newline\"><br><\/div>\\(\\begin{array}{cccccc}&amp; &amp; &amp; \\hfill \\phantom{\\rule{3em}{0ex}}f\\left(x\\right)&amp; =\\hfill &amp; \\sqrt{2x-1}\\hfill \\\\ \\text{To evaluate}\\phantom{\\rule{0.2em}{0ex}}f\\left(5\\right),\\phantom{\\rule{0.2em}{0ex}}\\text{substitute 5 for}\\phantom{\\rule{0.2em}{0ex}}x.\\hfill &amp; &amp; &amp; \\hfill \\phantom{\\rule{3em}{0ex}}f\\left(5\\right)&amp; =\\hfill &amp; \\sqrt{2\u00b75-1}\\hfill \\\\ \\text{Simplify.}\\hfill &amp; &amp; &amp; \\hfill \\phantom{\\rule{3em}{0ex}}f\\left(5\\right)&amp; =\\hfill &amp; \\sqrt{9}\\hfill \\\\ \\text{Take the square root.}\\hfill &amp; &amp; &amp; \\hfill \\phantom{\\rule{3em}{0ex}}f\\left(5\\right)&amp; =\\hfill &amp; 3\\hfill \\end{array}\\)<p id=\"fs-id1169143231118\"><span class=\"token\">\u24d1<\/span><\/p><div data-type=\"newline\"><br><\/div>\\(\\begin{array}{cccccc}&amp; &amp; &amp; \\hfill \\phantom{\\rule{1.5em}{0ex}}f\\left(x\\right)&amp; =\\hfill &amp; \\sqrt{2x-1}\\hfill \\\\ \\text{To evaluate}\\phantom{\\rule{0.2em}{0ex}}f\\left(-2\\right),\\phantom{\\rule{0.2em}{0ex}}\\text{substitute}\\phantom{\\rule{0.2em}{0ex}}-2\\phantom{\\rule{0.2em}{0ex}}\\text{for}\\phantom{\\rule{0.2em}{0ex}}x.\\hfill &amp; &amp; &amp; \\hfill \\phantom{\\rule{1.5em}{0ex}}f\\left(-2\\right)&amp; =\\hfill &amp; \\sqrt{2\\left(-2\\right)-1}\\hfill \\\\ \\text{Simplify.}\\hfill &amp; &amp; &amp; \\hfill \\phantom{\\rule{1.5em}{0ex}}f\\left(-2\\right)&amp; =\\hfill &amp; \\sqrt{-5}\\hfill \\end{array}\\)<p id=\"fs-id1169148229400\">Since the square root of a negative number is not a real number, the function does not have a value at \\(x=-2.\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1169145620857\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1169147879034\"><div data-type=\"problem\" id=\"fs-id1169148248313\"><p id=\"fs-id1169148063652\">For the function \\(f\\left(x\\right)=\\sqrt{3x-2},\\) find <span class=\"token\">\u24d0<\/span> \\(f\\left(6\\right)\\) <span class=\"token\">\u24d1<\/span> \\(f\\left(0\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169145498016\"><p><span class=\"token\">\u24d0<\/span>\\(f\\left(6\\right)=4\\)<span class=\"token\">\u24d1<\/span> no value at \\(x=0\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1169147796778\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1169147765727\"><div data-type=\"problem\" id=\"fs-id1169147859022\"><p id=\"fs-id1169145988381\">For the function \\(g\\left(x\\right)=\\sqrt{5x+5},\\) find <span class=\"token\">\u24d0<\/span> \\(g\\left(4\\right)\\) <span class=\"token\">\u24d1<\/span> \\(g\\left(-3\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169145623485\"><p id=\"fs-id1169145586011\"><span class=\"token\">\u24d0<\/span>\\(g\\left(4\\right)=5\\)<span class=\"token\">\u24d1<\/span> no value at \\(f\\left(-3\\right)\\)<\/p><\/div><\/div><\/div><p id=\"fs-id1169147987998\">We follow the same procedure to evaluate cube roots.<\/p><div data-type=\"example\" id=\"fs-id1169145664723\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1169147820779\"><div data-type=\"problem\" id=\"fs-id1169147877799\"><p id=\"fs-id1169145715326\">For the function \\(g\\left(x\\right)=\\sqrt[3]{x-6},\\) find <span class=\"token\">\u24d0<\/span> \\(g\\left(14\\right)\\) <span class=\"token\">\u24d1<\/span> \\(g\\left(-2\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169147745183\"><p id=\"fs-id1169148207457\"><span class=\"token\">\u24d0<\/span><\/p><div data-type=\"newline\"><br><\/div>\\(\\begin{array}{cccccc}&amp; &amp; &amp; \\hfill \\phantom{\\rule{0.5em}{0ex}}g\\left(x\\right)&amp; =\\hfill &amp; \\sqrt[3]{x-6}\\hfill \\\\ \\text{To evaluate}\\phantom{\\rule{0.2em}{0ex}}g\\left(14\\right),\\phantom{\\rule{0.2em}{0ex}}\\text{substitute 14 for}\\phantom{\\rule{0.2em}{0ex}}x.\\hfill &amp; &amp; &amp; \\hfill \\phantom{\\rule{0.5em}{0ex}}g\\left(14\\right)&amp; =\\hfill &amp; \\sqrt[3]{14-6}\\hfill \\\\ \\text{Simplify.}\\hfill &amp; &amp; &amp; \\hfill \\phantom{\\rule{0.5em}{0ex}}g\\left(14\\right)&amp; =\\hfill &amp; \\sqrt[3]{8}\\hfill \\\\ \\text{Take the cube root.}\\hfill &amp; &amp; &amp; \\hfill \\phantom{\\rule{0.5em}{0ex}}g\\left(14\\right)&amp; =\\hfill &amp; 2\\hfill \\end{array}\\)<p id=\"fs-id1169143763234\"><span class=\"token\">\u24d1<\/span><\/p><div data-type=\"newline\"><br><\/div>\\(\\begin{array}{cccccc}&amp; &amp; &amp; \\hfill g\\left(x\\right)&amp; =\\hfill &amp; \\sqrt[3]{x-6}\\hfill \\\\ \\text{To evaluate}\\phantom{\\rule{0.2em}{0ex}}g\\left(-2\\right),\\phantom{\\rule{0.2em}{0ex}}\\text{substitute}\\phantom{\\rule{0.2em}{0ex}}-2\\phantom{\\rule{0.2em}{0ex}}\\text{for}\\phantom{\\rule{0.2em}{0ex}}x.\\hfill &amp; &amp; &amp; \\hfill g\\left(-2\\right)&amp; =\\hfill &amp; \\sqrt[3]{-2-6}\\hfill \\\\ \\text{Simplify.}\\hfill &amp; &amp; &amp; \\hfill g\\left(-2\\right)&amp; =\\hfill &amp; \\sqrt[3]{-8}\\hfill \\\\ \\text{Take the cube root.}\\hfill &amp; &amp; &amp; \\hfill g\\left(-2\\right)&amp; =\\hfill &amp; -2\\hfill \\end{array}\\)<\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1169143573107\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1169147843527\"><div data-type=\"problem\" id=\"fs-id1169145575010\"><p id=\"fs-id1169145714216\">For the function \\(g\\left(x\\right)=\\sqrt[3]{3x-4},\\) find <span class=\"token\">\u24d0<\/span> \\(g\\left(4\\right)\\) <span class=\"token\">\u24d1<\/span> \\(g\\left(1\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169145644143\"><p id=\"fs-id1169145779297\"><span class=\"token\">\u24d0<\/span>\\(g\\left(4\\right)=2\\)<span class=\"token\">\u24d1<\/span>\\(g\\left(1\\right)=-1\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1169147833350\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1169145733809\"><div data-type=\"problem\" id=\"fs-id1169147825232\"><p id=\"fs-id1169148229294\">For the function \\(h\\left(x\\right)=\\sqrt[3]{5x-2},\\) find <span class=\"token\">\u24d0<\/span> \\(h\\left(2\\right)\\) <span class=\"token\">\u24d1<\/span> \\(h\\left(-5\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169147727895\"><p id=\"fs-id1169143550222\"><span class=\"token\">\u24d0<\/span>\\(h\\left(2\\right)=2\\)<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span>\\(h\\left(-5\\right)=-3\\)<\/div><\/div><\/div><p id=\"fs-id1169148124976\">The next example has fourth roots.<\/p><div data-type=\"example\" id=\"fs-id1169145667545\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1169145620381\"><div data-type=\"problem\" id=\"fs-id1169147806731\"><p id=\"fs-id1169145574634\">For the function \\(f\\left(x\\right)=\\sqrt[4]{5x-4},\\) find <span class=\"token\">\u24d0<\/span> \\(f\\left(4\\right)\\) <span class=\"token\">\u24d1<\/span> \\(f\\left(-12\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169148233330\"><p id=\"fs-id1169148229060\"><span class=\"token\">\u24d0<\/span><\/p><div data-type=\"newline\"><br><\/div>\\(\\begin{array}{cccccc}&amp; &amp; &amp; \\hfill \\phantom{\\rule{3.5em}{0ex}}f\\left(x\\right)&amp; =\\hfill &amp; \\sqrt[4]{5x-4}\\hfill \\\\ \\text{To evaluate}\\phantom{\\rule{0.2em}{0ex}}f\\left(4\\right),\\phantom{\\rule{0.2em}{0ex}}\\text{substitute 4 for}\\phantom{\\rule{0.2em}{0ex}}x.\\hfill &amp; &amp; &amp; \\hfill \\phantom{\\rule{3.5em}{0ex}}f\\left(4\\right)&amp; =\\hfill &amp; \\sqrt[4]{5\u00b74-4}\\hfill \\\\ \\text{Simplify.}\\hfill &amp; &amp; &amp; \\hfill \\phantom{\\rule{3.5em}{0ex}}f\\left(4\\right)&amp; =\\hfill &amp; \\sqrt[4]{16}\\hfill \\\\ \\text{Take the fourth root.}\\hfill &amp; &amp; &amp; \\hfill \\phantom{\\rule{3.5em}{0ex}}f\\left(4\\right)&amp; =\\hfill &amp; 2\\hfill \\end{array}\\)<p id=\"fs-id1169147841823\"><span class=\"token\">\u24d1<\/span><\/p><div data-type=\"newline\"><br><\/div>\\(\\begin{array}{cccccc}&amp; &amp; &amp; \\hfill f\\left(x\\right)&amp; =\\hfill &amp; \\sqrt[4]{5x-4}\\hfill \\\\ \\text{To evaluate}\\phantom{\\rule{0.2em}{0ex}}f\\left(-12\\right),\\phantom{\\rule{0.2em}{0ex}}\\text{substitute}\\phantom{\\rule{0.2em}{0ex}}-12\\phantom{\\rule{0.2em}{0ex}}\\text{for}\\phantom{\\rule{0.2em}{0ex}}x.\\hfill &amp; &amp; &amp; \\hfill f\\left(-12\\right)&amp; =\\hfill &amp; \\sqrt[4]{5\\left(-12\\right)-4}\\hfill \\\\ \\text{Simplify.}\\hfill &amp; &amp; &amp; \\hfill f\\left(-12\\right)&amp; =\\hfill &amp; \\sqrt[4]{-64}\\hfill \\end{array}\\)<p id=\"fs-id1169143638539\">Since the fourth root of a negative number is not a real number, the function does not have a value at \\(x=-12.\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1169145946189\"><div data-type=\"problem\" id=\"fs-id1169147850137\"><p id=\"fs-id1169147847536\">For the function \\(f\\left(x\\right)=\\sqrt[4]{3x+4},\\) find <span class=\"token\">\u24d0<\/span> \\(f\\left(4\\right)\\) <span class=\"token\">\u24d1<\/span> \\(f\\left(-1\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169147806247\"><p id=\"fs-id1169147774929\"><span class=\"token\">\u24d0<\/span>\\(f\\left(4\\right)=2\\)<span class=\"token\">\u24d1<\/span>\\(f\\left(-1\\right)=1\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1169147707374\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1169143317888\"><div data-type=\"problem\" id=\"fs-id1169147906250\"><p id=\"fs-id1169147843734\">For the function \\(g\\left(x\\right)=\\sqrt[4]{5x+1},\\) find <span class=\"token\">\u24d0<\/span> \\(g\\left(16\\right)\\) <span class=\"token\">\u24d1<\/span> \\(g\\left(3\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169147979561\"><p id=\"fs-id1169142122817\"><span class=\"token\">\u24d0<\/span>\\(g\\left(16\\right)=3\\)<span class=\"token\">\u24d1<\/span>\\(g\\left(3\\right)=2\\)<\/p><\/div><\/div><\/div><\/div><div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1169147775047\"><h3 data-type=\"title\">Find the Domain of a Radical Function<\/h3><p id=\"fs-id1169147824778\">To find the <span data-type=\"term\" class=\"no-emphasis\">domain<\/span> and <span data-type=\"term\" class=\"no-emphasis\">range<\/span> of radical functions, we use our properties of radicals. For a radical with an even index, we said the radicand had to be greater than or equal to zero as even roots of negative numbers are not real numbers. For an odd index, the radicand can be any real number. We restate the properties here for reference.<\/p><div data-type=\"note\" id=\"fs-id1169148047556\"><div data-type=\"title\">Properties of \\(\\sqrt[n]{a}\\)<\/div><p id=\"fs-id1169147835801\">When <em data-effect=\"italics\">n<\/em> is an <strong data-effect=\"bold\">even<\/strong> number and:<\/p><ul id=\"fs-id1169147848685\" data-bullet-style=\"bullet\"><li>\\(a\\ge 0,\\) then \\(\\sqrt[n]{a}\\) is a real number.<\/li><li>\\(a&lt;0,\\) then \\(\\sqrt[n]{a}\\) is not a real number.<\/li><\/ul><p id=\"fs-id1169147763639\">When <em data-effect=\"italics\">n<\/em> is an <strong data-effect=\"bold\">odd<\/strong> number, \\(\\sqrt[n]{a}\\) is a real number for all values of <em data-effect=\"italics\">a<\/em>.<\/p><\/div><p id=\"fs-id1169147865230\">So, to find the domain of a radical function with even index, we set the radicand to be greater than or equal to zero. For an odd index radical, the radicand can be any real number.<\/p><div data-type=\"note\" id=\"fs-id1169147837500\"><div data-type=\"title\">Domain of a Radical Function<\/div><p id=\"fs-id1169147745047\">When the <strong data-effect=\"bold\">index<\/strong> of the radical is <strong data-effect=\"bold\">even<\/strong>, the radicand must be greater than or equal to zero.<\/p><p id=\"fs-id1169143550091\">When the <strong data-effect=\"bold\">index<\/strong> of the radical is <strong data-effect=\"bold\">odd<\/strong>, the radicand can be any real number.<\/p><\/div><div data-type=\"example\" id=\"fs-id1169145747305\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1169145730306\"><div data-type=\"problem\" id=\"fs-id1169147711453\"><p id=\"fs-id1169145620583\">Find the domain of the function, \\(f\\left(x\\right)=\\sqrt{3x-4}.\\) Write the domain in interval notation.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169145499784\"><p id=\"fs-id1169147809361\">Since the function, \\(f\\left(x\\right)=\\sqrt{3x-4}\\) has a radical with an index of 2, which is even, we know the radicand must be greater than or equal to 0. We set the radicand to be greater than or equal to 0 and then solve to find the domain.<\/p><p id=\"fs-id1169147826910\">\\(\\begin{array}{cccccccc}&amp; &amp; &amp; &amp; &amp; \\hfill 3x-4&amp; \\ge \\hfill &amp; 0\\hfill \\\\ \\text{Solve.}\\hfill &amp; &amp; &amp; &amp; &amp; \\hfill 3x&amp; \\ge \\hfill &amp; 4\\hfill \\\\ &amp; &amp; &amp; &amp; &amp; \\hfill x&amp; \\ge \\hfill &amp; \\frac{4}{3}\\hfill \\end{array}\\)<\/p><p id=\"fs-id1169143577542\">The domain of \\(f\\left(x\\right)=\\sqrt{3x-4}\\) is all values \\(x\\ge \\frac{4}{3}\\) and we write it in interval notation as \\(\\left[\\frac{4}{3},\\infty \\right).\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1169145520198\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1169145644630\"><div data-type=\"problem\" id=\"fs-id1169147959847\"><p id=\"fs-id1169148210160\">Find the domain of the function, \\(f\\left(x\\right)=\\sqrt{6x-5}.\\) Write the domain in interval notation.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169148037760\"><p id=\"fs-id1169148251259\">\\(\\left[\\frac{5}{6},\\infty \\right)\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1169147909572\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1169145550678\"><div data-type=\"problem\" id=\"fs-id1169147860226\"><p id=\"fs-id1169148115867\">Find the domain of the function, \\(f\\left(x\\right)=\\sqrt{4-5x}.\\) Write the domain in interval notation.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169147838012\"><p id=\"fs-id1169147852288\">\\(\\left(\\text{\u2212}\\infty ,\\frac{4}{5}\\right]\\)<\/p><\/div><\/div><\/div><div data-type=\"example\" id=\"fs-id1169147764891\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1169143601638\"><div data-type=\"problem\" id=\"fs-id1169145574085\"><p id=\"fs-id1169145716676\">Find the domain of the function, \\(g\\left(x\\right)=\\sqrt{\\frac{6}{x-1}}.\\) Write the domain in interval notation.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169148248332\"><p id=\"fs-id1169147738757\">Since the function, \\(g\\left(x\\right)=\\sqrt{\\frac{6}{x-1}}\\) has a radical with an index of 2, which is even, we know the radicand must be greater than or equal to 0.<\/p><p id=\"fs-id1169143330161\">The radicand cannot be zero since the numerator is not zero.<\/p><p id=\"fs-id1169145608090\">For \\(\\frac{6}{x-1}\\) to be greater than zero, the denominator must be positive since the numerator is positive. We know a positive divided by a positive is positive.<\/p><p id=\"fs-id1169147731977\">We set \\(x-1&gt;0\\) and solve.<\/p><p id=\"fs-id1169143487387\">\\(\\begin{array}{cccccccc}&amp; &amp; &amp; &amp; &amp; \\hfill x-1&amp; &gt;\\hfill &amp; 0\\hfill \\\\ \\text{Solve.}\\hfill &amp; &amp; &amp; &amp; &amp; \\hfill x&amp; &gt;\\hfill &amp; 1\\hfill \\end{array}\\)<\/p><p id=\"fs-id1169145507872\">Also, since the radicand is a fraction, we must realize that the denominator cannot be zero.<\/p><p id=\"fs-id1169147817212\">We solve \\(x-1=0\\) to find the value that must be eliminated from the domain.<\/p><p id=\"fs-id1169147758791\">\\(\\begin{array}{cccccccc}&amp; &amp; &amp; &amp; &amp; \\hfill x-1&amp; =\\hfill &amp; 0\\hfill \\\\ \\text{Solve.}\\hfill &amp; &amp; &amp; &amp; &amp; \\hfill x&amp; =\\hfill &amp; 1\\phantom{\\rule{0.2em}{0ex}}\\text{so}\\phantom{\\rule{0.2em}{0ex}}x\\ne 1\\phantom{\\rule{0.2em}{0ex}}\\text{in the domain.}\\hfill \\end{array}\\)<\/p><p id=\"fs-id1169143578779\">Putting this together we get the domain is \\(x&gt;1\\) and we write it as \\(\\left(1,\\infty \\right).\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1169145665511\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1169147777460\"><div data-type=\"problem\" id=\"fs-id1169148224616\"><p id=\"fs-id1169147875579\">Find the domain of the function, \\(f\\left(x\\right)=\\sqrt{\\frac{4}{x+3}}.\\) Write the domain in interval notation.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169148101058\"><p id=\"fs-id1169147946981\">\\(\\left(-3,\\infty \\right)\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1169147802653\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1169147764968\"><div data-type=\"problem\" id=\"fs-id1169147965038\"><p id=\"fs-id1169142263113\">Find the domain of the function, \\(h\\left(x\\right)=\\sqrt{\\frac{9}{x-5}}.\\) Write the domain in interval notation.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169148211614\"><p id=\"fs-id1169145505677\">\\(\\left(5,\\infty \\right)\\)<\/p><\/div><\/div><\/div><p id=\"fs-id1169147962378\">The next example involves a cube root and so will require different thinking.<\/p><div data-type=\"example\" id=\"fs-id1169147833926\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1169147768127\"><div data-type=\"problem\" id=\"fs-id1169145621716\"><p id=\"fs-id1169145580555\">Find the domain of the function, \\(f\\left(x\\right)=\\sqrt[3]{2{x}^{2}+3}.\\) Write the domain in interval notation.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169147700003\"><p id=\"fs-id1169147947059\">Since the function, \\(f\\left(x\\right)=\\sqrt[3]{2{x}^{2}+3}\\) has a radical with an index of 3, which is odd, we know the radicand can be any real number. This tells us the domain is any real number. In interval notation, we write \\(\\left(\\text{\u2212}\\infty ,\\infty \\right).\\)<\/p><p id=\"fs-id1169147980456\">The domain of \\(f\\left(x\\right)=\\sqrt[3]{2{x}^{2}+3}\\) is all real numbers and we write it in interval notation as \\(\\left(\\text{\u2212}\\infty ,\\infty \\right).\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1169145733006\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1169143502868\"><div data-type=\"problem\" id=\"fs-id1169147707473\"><p id=\"fs-id1169147864365\">Find the domain of the function, \\(f\\left(x\\right)=\\sqrt[3]{3{x}^{2}-1}.\\) Write the domain in interval notation.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169147837932\"><p id=\"fs-id1169145620600\">\\(\\left(\\text{\u2212}\\infty ,\\infty \\right)\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1169147827855\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1169148077672\"><div data-type=\"problem\" id=\"fs-id1169148116396\"><p id=\"fs-id1169145670713\">Find the domain of the function, \\(g\\left(x\\right)=\\sqrt[3]{5x-4}.\\) Write the domain in interval notation.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169147804280\"><p id=\"fs-id1169147837605\">\\(\\left(\\text{\u2212}\\infty ,\\infty \\right)\\)<\/p><\/div><\/div><\/div><\/div><div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1169147772022\"><h3 data-type=\"title\">Graph Radical Functions<\/h3><p id=\"fs-id1169148251663\">Before we graph any radical function, we first find the <span data-type=\"term\" class=\"no-emphasis\">domain<\/span> of the function. For the function, \\(f\\left(x\\right)=\\sqrt{x},\\) the index is even, and so the radicand must be greater than or equal to 0.<\/p><p id=\"fs-id1169145506488\">This tells us the domain is \\(x\\ge 0\\) and we write this in interval notation as \\(\\left[0,\\infty \\right).\\)<\/p><p id=\"fs-id1169142400725\">Previously we used point plotting to graph the function, \\(f\\left(x\\right)=\\sqrt{x}.\\) We chose <em data-effect=\"italics\">x<\/em>-values, substituted them in and then created a chart. Notice we chose points that are perfect squares in order to make taking the square root easier.<\/p><span data-type=\"media\" id=\"fs-id1169148231243\" data-alt=\"The figure shows the square root function graph on the x y-coordinate plane. The x-axis of the plane runs from 0 to 7. The y-axis runs from 0 to 7. The function has a starting point at (0, 0) and goes through the points (1, 1) and (4, 2). A table is shown beside the graph with 3 columns and 5 rows. The first row is a header row with the expressions \u201cx\u201d, \u201cf (x) = square root of x\u201d, and \u201c(x, f (x))\u201d. The second row has the numbers 0, 0, and (0, 0). The third row has the numbers 1, 1, and (1, 1). The fourth row has the numbers 4, 2, and (4, 2). The fifth row has the numbers 9, 3, and (9, 3).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_08_07_001_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows the square root function graph on the x y-coordinate plane. The x-axis of the plane runs from 0 to 7. The y-axis runs from 0 to 7. The function has a starting point at (0, 0) and goes through the points (1, 1) and (4, 2). A table is shown beside the graph with 3 columns and 5 rows. The first row is a header row with the expressions \u201cx\u201d, \u201cf (x) = square root of x\u201d, and \u201c(x, f (x))\u201d. The second row has the numbers 0, 0, and (0, 0). The third row has the numbers 1, 1, and (1, 1). The fourth row has the numbers 4, 2, and (4, 2). The fifth row has the numbers 9, 3, and (9, 3).\"><\/span><p id=\"fs-id1169147774393\">Once we see the graph, we can find the range of the function. The <em data-effect=\"italics\">y<\/em>-values of the function are greater than or equal to zero. The range then is \\(\\left[0,\\infty \\right).\\)<\/p><div data-type=\"example\" id=\"fs-id1169148132081\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1169148072142\"><div data-type=\"problem\" id=\"fs-id1169147830798\"><p id=\"fs-id1169145775018\">For the function \\(f\\left(x\\right)=\\sqrt{x+3},\\)<\/p><p id=\"fs-id1169145735236\"><span class=\"token\">\u24d0<\/span> find the domain <span class=\"token\">\u24d1<\/span> graph the function <span class=\"token\">\u24d2<\/span> use the graph to determine the range.<\/p><\/div><div data-type=\"solution\"><p id=\"fs-id1169147959625\"><span class=\"token\">\u24d0<\/span> Since the radical has index 2, we know the radicand must be greater than or equal to zero. If \\(x+3\\ge 0,\\) then \\(x\\ge -3.\\) This tells us the domain is all values \\(x\\ge -3\\) and written in interval notation as \\(\\left[-3,\\infty \\right).\\)<\/p><p id=\"fs-id1169147787156\"><span class=\"token\">\u24d1<\/span> To graph the function, we choose points in the interval \\(\\left[-3,\\infty \\right)\\) that will also give us a radicand which will be easy to take the square root.<\/p><span data-type=\"media\" id=\"fs-id1169147716047\" data-alt=\"The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 3 to 3. The y-axis runs from 0 to 7. The function has a starting point at (negative 3, 0) and goes through the points (negative 2, 1) and (1, 2). A table is shown beside the graph with 3 columns and 5 rows. The first row is a header row with the expressions \u201cx\u201d, \u201cf (x) = square root of the quantity x plus 3\u201d, and \u201c(x, f (x))\u201d. The second row has the numbers negative 3, 0, and (negative 3, 0). The third row has the numbers negative 2, 1, and (negative 2, 1). The fourth row has the numbers 1, 2, and (1, 2). The fifth row has the numbers 6, 3, and (6, 3).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_08_07_002_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 3 to 3. The y-axis runs from 0 to 7. The function has a starting point at (negative 3, 0) and goes through the points (negative 2, 1) and (1, 2). A table is shown beside the graph with 3 columns and 5 rows. The first row is a header row with the expressions \u201cx\u201d, \u201cf (x) = square root of the quantity x plus 3\u201d, and \u201c(x, f (x))\u201d. The second row has the numbers negative 3, 0, and (negative 3, 0). The third row has the numbers negative 2, 1, and (negative 2, 1). The fourth row has the numbers 1, 2, and (1, 2). The fifth row has the numbers 6, 3, and (6, 3).\"><\/span><p id=\"fs-id1169147708185\"><span class=\"token\">\u24d2<\/span> Looking at the graph, we see the <em data-effect=\"italics\">y<\/em>-values of the function are greater than or equal to zero. The range then is \\(\\left[0,\\infty \\right).\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1169137906940\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1169147826840\"><div data-type=\"problem\" id=\"fs-id1169148069963\"><p id=\"fs-id1169147738653\">For the function \\(f\\left(x\\right)=\\sqrt{x+2},\\) <span class=\"token\">\u24d0<\/span> find the domain <span class=\"token\">\u24d1<\/span> graph the function <span class=\"token\">\u24d2<\/span> use the graph to determine the range.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169147834274\"><p id=\"fs-id1169145696314\"><span class=\"token\">\u24d0<\/span> domain: \\(\\left[-2,\\infty \\right)\\)<\/p><div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d1<\/span><div data-type=\"newline\"><br><\/div> <span data-type=\"media\" id=\"fs-id1169145660319\" data-alt=\"The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 2 to 6. The y-axis runs from 0 to 8. The function has a starting point at (negative 2, 0) and goes through the points (negative 1, 1) and (2, 2).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_08_07_301_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 2 to 6. The y-axis runs from 0 to 8. The function has a starting point at (negative 2, 0) and goes through the points (negative 1, 1) and (2, 2).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span> range: \\(\\left[0,\\infty \\right)\\)<\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1169145735224\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1169145731036\"><div data-type=\"problem\" id=\"fs-id1169147774570\"><p id=\"fs-id1169147836064\">For the function \\(f\\left(x\\right)=\\sqrt{x-2},\\) <span class=\"token\">\u24d0<\/span> find the domain <span class=\"token\">\u24d1<\/span> graph the function <span class=\"token\">\u24d2<\/span> use the graph to determine the range.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169145670796\"><p id=\"fs-id1169147906599\"><span class=\"token\">\u24d0<\/span> domain: \\(\\left[2,\\infty \\right)\\)<\/p><div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d1<\/span><div data-type=\"newline\"><br><\/div> <span data-type=\"media\" id=\"fs-id1169145969952\" data-alt=\"The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from 0 to 8. The y-axis runs from 0 to 6. The function has a starting point at (2, 0) and goes through the points (3, 1) and (6, 2).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_08_07_302_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from 0 to 8. The y-axis runs from 0 to 6. The function has a starting point at (2, 0) and goes through the points (3, 1) and (6, 2).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span> range: \\(\\left[0,\\infty \\right)\\)<\/div><\/div><\/div><p id=\"fs-id1169147759371\">In our previous work graphing functions, we graphed \\(f\\left(x\\right)={x}^{3}\\) but we did not graph the function \\(f\\left(x\\right)=\\sqrt[3]{x}.\\) We will do this now in the next example.<\/p><div data-type=\"example\" id=\"fs-id1169147876087\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1169147708819\"><div data-type=\"problem\" id=\"fs-id1169145844089\"><p id=\"fs-id1169148237468\">For the function \\(f\\left(x\\right)=\\sqrt[3]{x},\\) <span class=\"token\">\u24d0<\/span> find the domain <span class=\"token\">\u24d1<\/span> graph the function <span class=\"token\">\u24d2<\/span> use the graph to determine the range.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169147808469\"><p id=\"fs-id1169145643316\"><span class=\"token\">\u24d0<\/span> Since the radical has index 3, we know the radicand can be any real number. This tells us the domain is all real numbers and written in interval notation as \\(\\left(\\text{\u2212}\\infty ,\\infty \\right)\\)<\/p><p id=\"fs-id1169148054588\"><span class=\"token\">\u24d1<\/span> To graph the function, we choose points in the interval \\(\\left(\\text{\u2212}\\infty ,\\infty \\right)\\) that will also give us a radicand which will be easy to take the cube root.<\/p><span data-type=\"media\" id=\"fs-id1169147732107\" data-alt=\"The figure shows the cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The function has a center point at (0, 0) and goes through the points (1, 1), (negative 1, negative 1), (8, 2), and (negative 8, negative 2). A table is shown beside the graph with 3 columns and 6 rows. The first row is a header row with the expressions \u201cx\u201d, \u201cf (x) = cube root of x\u201d, and \u201c(x, f (x))\u201d. The second row has the numbers negative 8, negative 2, and (negative 8, negative 2). The third row has the numbers negative 1, negative 1, and (negative 1, negative 1). The fourth row has the numbers 0, 0, and (0, 0). The fifth row has the numbers 1, 1, and (1, 1). The sixth row has the numbers 8, 2, and (8, 2).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_08_07_003_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows the cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The function has a center point at (0, 0) and goes through the points (1, 1), (negative 1, negative 1), (8, 2), and (negative 8, negative 2). A table is shown beside the graph with 3 columns and 6 rows. The first row is a header row with the expressions \u201cx\u201d, \u201cf (x) = cube root of x\u201d, and \u201c(x, f (x))\u201d. The second row has the numbers negative 8, negative 2, and (negative 8, negative 2). The third row has the numbers negative 1, negative 1, and (negative 1, negative 1). The fourth row has the numbers 0, 0, and (0, 0). The fifth row has the numbers 1, 1, and (1, 1). The sixth row has the numbers 8, 2, and (8, 2).\"><\/span><p id=\"fs-id1169147846342\"><span class=\"token\">\u24d2<\/span> Looking at the graph, we see the <em data-effect=\"italics\">y<\/em>-values of the function are all real numbers. The range then is \\(\\left(\\text{\u2212}\\infty ,\\infty \\right).\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1169147741965\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1169147963259\"><div data-type=\"problem\" id=\"fs-id1169145924994\"><p id=\"fs-id1169145924996\">For the function \\(f\\left(x\\right)=\\text{\u2212}\\sqrt[3]{x},\\)<\/p><p id=\"fs-id1169147831008\"><span class=\"token\">\u24d0<\/span> find the domain <span class=\"token\">\u24d1<\/span> graph the function <span class=\"token\">\u24d2<\/span> use the graph to determine the range.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169141300257\"><p id=\"fs-id1169143448553\"><span class=\"token\">\u24d0<\/span> domain: \\(\\text{(}-\\infty ,\\infty \\right)\\)<\/p><div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d1<\/span><div data-type=\"newline\"><br><\/div> <span data-type=\"media\" id=\"fs-id1169142133180\" data-alt=\"The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 2 to 2. The y-axis runs from negative 2 to 2. The function has a center point at (0, 0) and goes through the points (1, negative 1) and (negative 1, 1).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_08_07_303_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 2 to 2. The y-axis runs from negative 2 to 2. The function has a center point at (0, 0) and goes through the points (1, negative 1) and (negative 1, 1).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span> range: \\(\\text{(}-\\infty ,\\infty \\right)\\)<\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1169147747631\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1169147868760\"><div data-type=\"problem\" id=\"fs-id1169147868762\"><p id=\"fs-id1169147877505\">For the function \\(f\\left(x\\right)=\\sqrt[3]{x-2},\\)<\/p><p id=\"fs-id1169142417273\"><span class=\"token\">\u24d0<\/span> find the domain <span class=\"token\">\u24d1<\/span> graph the function <span class=\"token\">\u24d2<\/span> use the graph to determine the range.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169147983988\"><p id=\"fs-id1169147983990\"><span class=\"token\">\u24d0<\/span> domain: \\(\\text{(}-\\infty ,\\infty \\right)\\)<\/p><div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d1<\/span><div data-type=\"newline\"><br><\/div> <span data-type=\"media\" id=\"fs-id1169148076410\" data-alt=\"The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 1 to 5. The y-axis runs from negative 3 to 3. The function has a center point at (2, 0) and goes through the points (1, negative 1) and (3, 2).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_08_07_304_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 1 to 5. The y-axis runs from negative 3 to 3. The function has a center point at (2, 0) and goes through the points (1, negative 1) and (3, 2).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span> range: \\(\\text{(}-\\infty ,\\infty \\right)\\)<\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1169147978659\" class=\"media-2\"><p id=\"fs-id1169148126317\">Access these online resources for additional instruction and practice with radical functions.<\/p><ul id=\"fs-id1169147948111\" data-display=\"block\"><li><a href=\"https:\/\/openstax.org\/l\/37RadFuncDom1\">Domain of a Radical Function<\/a><\/li><li><a href=\"https:\/\/openstax.org\/l\/37RadFuncDom2\">Domain of a Radical Function 2<\/a><\/li><li><a href=\"https:\/\/openstax.org\/l\/37RadFuncDom3\">Finding Domain of a Radical Function<\/a><\/li><\/ul><\/div><\/div><div class=\"textbox\" data-depth=\"1\" id=\"fs-id1169147743296\"><h3 data-type=\"title\">Key Concepts<\/h3><ul id=\"fs-id1169145717081\" data-bullet-style=\"bullet\"><li><strong data-effect=\"bold\">Properties of \\(\\sqrt[n]{a}\\)<\/strong><ul id=\"fs-id1169141036816\" data-bullet-style=\"bullet\"><li>When <em data-effect=\"italics\">n<\/em> is an <strong data-effect=\"bold\">even<\/strong> number and:<div data-type=\"newline\"><br><\/div> \\(a\\ge 0,\\) then \\(\\sqrt[n]{a}\\) is a real number.<div data-type=\"newline\"><br><\/div> \\(a&lt;0,\\) then \\(\\sqrt[n]{a}\\) is not a real number.<\/li><li>When <em data-effect=\"italics\">n<\/em> is an <strong data-effect=\"bold\">odd<\/strong> number, \\(\\sqrt[n]{a}\\) is a real number for all values of <em data-effect=\"italics\">a<\/em>.<\/li><\/ul><\/li><li><strong data-effect=\"bold\">Domain of a Radical Function<\/strong><ul id=\"fs-id1169145645013\" data-bullet-style=\"bullet\"><li>When the <strong data-effect=\"bold\">index<\/strong> of the radical is <strong data-effect=\"bold\">even<\/strong>, the radicand must be greater than or equal to zero.<\/li><li>When the <strong data-effect=\"bold\">index<\/strong> of the radical is <strong data-effect=\"bold\">odd<\/strong>, the radicand can be any real number.<\/li><\/ul><\/li><\/ul><\/div><div class=\"textbox\" data-depth=\"1\" id=\"fs-id1169148097720\"><div class=\"practice-perfect\" data-depth=\"2\" id=\"fs-id1169148231171\"><h4 data-type=\"title\">Practice Makes Perfect<\/h4><p id=\"fs-id1169148101448\"><strong data-effect=\"bold\">Evaluate a Radical Function<\/strong><\/p><p id=\"fs-id1169148209532\">In the following exercises, evaluate each function.<\/p><div data-type=\"exercise\" id=\"fs-id1169147743159\"><div data-type=\"problem\" id=\"fs-id1169145716402\"><p id=\"fs-id1169145716404\">\\(f\\left(x\\right)=\\sqrt{4x-4},\\) find<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span> \\(f\\left(5\\right)\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> \\(f\\left(0\\right).\\)<\/div><div data-type=\"solution\" id=\"fs-id1169147800145\"><p id=\"fs-id1169142281310\"><span class=\"token\">\u24d0<\/span>\\(f\\left(5\\right)=4\\)<span class=\"token\">\u24d1<\/span> no value at \\(x=0\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169142480106\"><div data-type=\"problem\" id=\"fs-id1169148101052\"><p id=\"fs-id1169148101054\">\\(f\\left(x\\right)=\\sqrt{6x-5},\\) find<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span> \\(f\\left(5\\right)\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> \\(f\\left(-1\\right).\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169148207439\"><div data-type=\"problem\" id=\"fs-id1169147804241\"><p id=\"fs-id1169145620467\">\\(g\\left(x\\right)=\\sqrt{6x+1},\\) find<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span> \\(g\\left(4\\right)\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> \\(g\\left(8\\right).\\)<\/div><div data-type=\"solution\" id=\"fs-id1169145507838\"><p id=\"fs-id1169143580099\"><span class=\"token\">\u24d0<\/span>\\(g\\left(4\\right)=5\\)<span class=\"token\">\u24d1<\/span>\\(g\\left(8\\right)=7\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169147909782\"><div data-type=\"problem\" id=\"fs-id1169147865255\"><p id=\"fs-id1169147865257\">\\(g\\left(x\\right)=\\sqrt{3x+1},\\) find<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span> \\(g\\left(8\\right)\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> \\(g\\left(5\\right).\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169145730224\"><div data-type=\"problem\" id=\"fs-id1169147758640\"><p id=\"fs-id1169147758642\">\\(F\\left(x\\right)=\\sqrt{3-2x},\\) find<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span> \\(F\\left(1\\right)\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> \\(F\\left(-11\\right).\\)<\/div><div data-type=\"solution\" id=\"fs-id1169148235035\"><p id=\"fs-id1169145505941\"><span class=\"token\">\u24d0<\/span>\\(F\\left(1\\right)=1\\)<span class=\"token\">\u24d1<\/span>\\(F\\left(-11\\right)=5\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169145643246\"><div data-type=\"problem\" id=\"fs-id1169145643248\"><p id=\"fs-id1169145644766\">\\(F\\left(x\\right)=\\sqrt{8-4x},\\) find<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span> \\(F\\left(1\\right)\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> \\(F\\left(-2\\right).\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169145844012\"><div data-type=\"problem\" id=\"fs-id1169148229326\"><p id=\"fs-id1169148229328\">\\(G\\left(x\\right)=\\sqrt{5x-1},\\) find<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span> \\(G\\left(5\\right)\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> \\(G\\left(2\\right).\\)<\/div><div data-type=\"solution\" id=\"fs-id1169147863238\"><p id=\"fs-id1169147863240\"><span class=\"token\">\u24d0<\/span>\\(G\\left(5\\right)=2\\sqrt{6}\\)<span class=\"token\">\u24d1<\/span>\\(G\\left(2\\right)=3\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169147768758\"><div data-type=\"problem\" id=\"fs-id1169148208329\"><p id=\"fs-id1169148208331\">\\(G\\left(x\\right)=\\sqrt{4x+1},\\) find<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span> \\(G\\left(11\\right)\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> \\(G\\left(2\\right).\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169147719067\"><div data-type=\"problem\" id=\"fs-id1169147719070\"><p id=\"fs-id1169147700129\">\\(g\\left(x\\right)=\\sqrt[3]{2x-4},\\) find<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span> \\(g\\left(6\\right)\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> \\(g\\left(-2\\right).\\)<\/div><div data-type=\"solution\" id=\"fs-id1169147977948\"><p id=\"fs-id1169147977950\"><span class=\"token\">\u24d0<\/span>\\(g\\left(6\\right)=2\\)<span class=\"token\">\u24d1<\/span>\\(g\\left(-2\\right)=-2\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169147949679\"><div data-type=\"problem\"><p id=\"fs-id1169145662640\">\\(g\\left(x\\right)=\\sqrt[3]{7x-1},\\) find<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span> \\(g\\left(4\\right)\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> \\(g\\left(-1\\right).\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169148229958\"><div data-type=\"problem\" id=\"fs-id1169148229960\"><p id=\"fs-id1169148229963\">\\(h\\left(x\\right)=\\sqrt[3]{{x}^{2}-4},\\) find<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span> \\(h\\left(-2\\right)\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> \\(h\\left(6\\right).\\)<\/div><div data-type=\"solution\" id=\"fs-id1169141298382\"><p id=\"fs-id1169141298384\"><span class=\"token\">\u24d0<\/span>\\(h\\left(-2\\right)=0\\)<span class=\"token\">\u24d1<\/span>\\(h\\left(6\\right)=2\\sqrt[3]{4}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169148233516\"><div data-type=\"problem\" id=\"fs-id1169143534313\"><p id=\"fs-id1169143534315\">\\(h\\left(x\\right)=\\sqrt[3]{{x}^{2}+4},\\) find<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span> \\(h\\left(-2\\right)\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> \\(h\\left(6\\right).\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169147750980\"><div data-type=\"problem\" id=\"fs-id1169147750982\"><p id=\"fs-id1169145843952\">For the function<\/p><div data-type=\"newline\"><br><\/div>\\(f\\left(x\\right)=\\sqrt[4]{2{x}^{3}},\\) find<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span> \\(f\\left(0\\right)\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> \\(f\\left(2\\right).\\)<\/div><div data-type=\"solution\" id=\"fs-id1169140999980\"><p id=\"fs-id1169140999982\"><span class=\"token\">\u24d0<\/span>\\(f\\left(0\\right)=0\\)<span class=\"token\">\u24d1<\/span>\\(f\\left(2\\right)=2\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169145578894\"><div data-type=\"problem\" id=\"fs-id1169147878606\"><p id=\"fs-id1169147878608\">For the function<\/p><div data-type=\"newline\"><br><\/div>\\(f\\left(x\\right)=\\sqrt[4]{3{x}^{3}},\\) find<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span> \\(f\\left(0\\right)\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> \\(f\\left(3\\right).\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169143303481\"><div data-type=\"problem\" id=\"fs-id1169143303483\"><p id=\"fs-id1169143303485\">For the function<\/p><div data-type=\"newline\"><br><\/div>\\(g\\left(x\\right)=\\sqrt[4]{4-4x},\\) find<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span> \\(g\\left(1\\right)\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> \\(g\\left(-3\\right).\\)<\/div><div data-type=\"solution\" id=\"fs-id1169143520298\"><p id=\"fs-id1169145640196\"><span class=\"token\">\u24d0<\/span>\\(g\\left(1\\right)=0\\)<span class=\"token\">\u24d1<\/span>\\(g\\left(-3\\right)=2\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169147966879\"><div data-type=\"problem\" id=\"fs-id1169143614137\"><p id=\"fs-id1169143614139\">For the function<\/p><div data-type=\"newline\"><br><\/div>\\(g\\left(x\\right)=\\sqrt[4]{8-4x},\\) find<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span> \\(g\\left(-6\\right)\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> \\(g\\left(2\\right).\\)<\/div><\/div><p id=\"fs-id1169142246848\"><strong data-effect=\"bold\">Find the Domain of a Radical Function<\/strong><\/p><p id=\"fs-id1169143520330\">In the following exercises, find the domain of the function and write the domain in interval notation.<\/p><div data-type=\"exercise\" id=\"fs-id1169143520333\"><div data-type=\"problem\" id=\"fs-id1169143520335\"><p id=\"fs-id1169143520337\">\\(f\\left(x\\right)=\\sqrt{3x-1}\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169141036432\"><p id=\"fs-id1169141036434\">\\(\\left[\\frac{1}{3},\\infty \\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169148229556\"><div data-type=\"problem\" id=\"fs-id1169141030517\"><p id=\"fs-id1169141030519\">\\(f\\left(x\\right)=\\sqrt{4x-2}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169147816115\"><div data-type=\"problem\" id=\"fs-id1169147816117\"><p id=\"fs-id1169147816119\">\\(g\\left(x\\right)=\\sqrt{2-3x}\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169143492471\"><p id=\"fs-id1169148230560\">\\(\\left(\\text{\u2212}\\infty ,\\frac{2}{3}\\right]\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169143576214\"><div data-type=\"problem\" id=\"fs-id1169147849778\"><p id=\"fs-id1169147849780\">\\(g\\left(x\\right)=\\sqrt{8-x}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169142417344\"><div data-type=\"problem\" id=\"fs-id1169142417346\"><p id=\"fs-id1169142417348\">\\(h\\left(x\\right)=\\sqrt{\\frac{5}{x-2}}\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169145747993\"><p id=\"fs-id1169145747996\">\\(\\left(2,\\infty \\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169145494672\"><div data-type=\"problem\" id=\"fs-id1169145494674\"><p id=\"fs-id1169145494676\">\\(h\\left(x\\right)=\\sqrt{\\frac{6}{x+3}}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169145621319\"><div data-type=\"problem\" id=\"fs-id1169143305828\"><p id=\"fs-id1169143305830\">\\(f\\left(x\\right)=\\sqrt{\\frac{x+3}{x-2}}\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169148125882\"><p id=\"fs-id1169148125884\">\\(\\left(\\text{\u2212}\\infty ,-3\\right]\\cup \\left(2,\\infty \\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169147878752\"><div data-type=\"problem\" id=\"fs-id1169147878754\"><p id=\"fs-id1169141015076\">\\(f\\left(x\\right)=\\sqrt{\\frac{x-1}{x+4}}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169141298449\"><div data-type=\"problem\" id=\"fs-id1169141298451\"><p id=\"fs-id1169141298453\">\\(g\\left(x\\right)=\\sqrt[3]{8x-1}\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169147841328\"><p id=\"fs-id1169147841330\">\\(\\left(\\text{\u2212}\\infty ,\\infty \\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169143581471\"><div data-type=\"problem\" id=\"fs-id1169143581474\"><p id=\"fs-id1169143581476\">\\(g\\left(x\\right)=\\sqrt[3]{6x+5}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169141036489\"><div data-type=\"problem\" id=\"fs-id1169141036492\"><p id=\"fs-id1169141036494\">\\(f\\left(x\\right)=\\sqrt[3]{4{x}^{2}-16}\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169145494092\"><p id=\"fs-id1169145494094\">\\(\\left(\\text{\u2212}\\infty ,\\infty \\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169143533398\"><div data-type=\"problem\" id=\"fs-id1169143533400\"><p id=\"fs-id1169145608627\">\\(f\\left(x\\right)=\\sqrt[3]{6{x}^{2}-25}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169143614237\"><div data-type=\"problem\" id=\"fs-id1169143614239\"><p id=\"fs-id1169143614154\">\\(F\\left(x\\right)=\\sqrt[4]{8x+3}\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169143305858\"><p id=\"fs-id1169143305860\">\\(\\left[-\\frac{3}{8},\\infty \\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169148097678\"><div data-type=\"problem\" id=\"fs-id1169148097680\"><p id=\"fs-id1169148097682\">\\(F\\left(x\\right)=\\sqrt[4]{10-7x}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169145785903\"><div data-type=\"problem\" id=\"fs-id1169145785905\"><p id=\"fs-id1169145785908\">\\(G\\left(x\\right)=\\sqrt[5]{2x-1}\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169141015060\"><p id=\"fs-id1169141015062\">\\(\\left(\\text{\u2212}\\infty ,\\infty \\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169147947981\"><div data-type=\"problem\" id=\"fs-id1169147947983\"><p id=\"fs-id1169147947985\">\\(G\\left(x\\right)=\\sqrt[5]{6x-3}\\)<\/p><\/div><\/div><p id=\"fs-id1169147878727\"><strong data-effect=\"bold\">Graph Radical Functions<\/strong><\/p><p id=\"fs-id1169143681608\">In the following exercises, <span class=\"token\">\u24d0<\/span> find the domain of the function <span class=\"token\">\u24d1<\/span> graph the function <span class=\"token\">\u24d2<\/span> use the graph to determine the range.<\/p><div data-type=\"exercise\" id=\"fs-id1169143681624\"><div data-type=\"problem\" id=\"fs-id1169143681627\"><p id=\"fs-id1169143681629\">\\(f\\left(x\\right)=\\sqrt{x+1}\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169148218613\"><p id=\"fs-id1169148218615\"><span class=\"token\">\u24d0<\/span> domain: \\(\\left[-1,\\infty \\right)\\)<\/p><div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d1<\/span><div data-type=\"newline\"><br><\/div> <span data-type=\"media\" id=\"fs-id1169148132216\" data-alt=\"The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 1 to 7. The y-axis runs from negative 2 to 10. The function has a starting point at (negative 1, 0) and goes through the points (0, 1) and (3, 2).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_08_07_305_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 1 to 7. The y-axis runs from negative 2 to 10. The function has a starting point at (negative 1, 0) and goes through the points (0, 1) and (3, 2).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span>\\(\\left[0,\\infty \\right)\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169148117665\"><div data-type=\"problem\" id=\"fs-id1169148117667\"><p id=\"fs-id1169148117669\">\\(f\\left(x\\right)=\\sqrt{x-1}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169145720248\"><div data-type=\"problem\" id=\"fs-id1169145720250\"><p id=\"fs-id1169145720252\">\\(g\\left(x\\right)=\\sqrt{x+4}\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169148125839\"><p id=\"fs-id1169148125841\"><span class=\"token\">\u24d0<\/span> domain: \\(\\left[-4,\\infty \\right)\\)<\/p><div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d1<\/span><div data-type=\"newline\"><br><\/div> <span data-type=\"media\" id=\"fs-id1169143614188\" data-alt=\"The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 2 to 6. The function has a starting point at (negative 4, 0) and goes through the points (negative 3, 1) and (0, 2).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_08_07_307_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 2 to 6. The function has a starting point at (negative 4, 0) and goes through the points (negative 3, 1) and (0, 2).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span>\\(\\left[0,\\infty \\right)\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169141047999\"><div data-type=\"problem\" id=\"fs-id1169141048001\"><p id=\"fs-id1169141048004\">\\(g\\left(x\\right)=\\sqrt{x-4}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169145925291\"><div data-type=\"problem\" id=\"fs-id1169145925293\"><p id=\"fs-id1169145925295\">\\(f\\left(x\\right)=\\sqrt{x}+2\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169145925320\"><p id=\"fs-id1169141472915\"><span class=\"token\">\u24d0<\/span> domain: \\(\\left[0,\\infty \\right)\\)<\/p><div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d1<\/span><div data-type=\"newline\"><br><\/div> <span data-type=\"media\" id=\"fs-id1169141472943\" data-alt=\"The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from 0 to 8. The y-axis runs from 0 to 8. The function has a starting point at (0, 2) and goes through the points (1, 3) and (4, 4).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_08_07_309_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from 0 to 8. The y-axis runs from 0 to 8. The function has a starting point at (0, 2) and goes through the points (1, 3) and (4, 4).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span>\\(\\left[2,\\infty \\right)\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169143637756\"><div data-type=\"problem\" id=\"fs-id1169143637759\"><p id=\"fs-id1169143637761\">\\(f\\left(x\\right)=\\sqrt{x}-2\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169148096679\"><div data-type=\"problem\" id=\"fs-id1169148096681\"><p id=\"fs-id1169148096683\">\\(g\\left(x\\right)=2\\sqrt{x}\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169148096706\"><p id=\"fs-id1169148096708\"><span class=\"token\">\u24d0<\/span> domain: \\(\\left[0,\\infty \\right)\\)<\/p><div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d1<\/span><div data-type=\"newline\"><br><\/div> <span data-type=\"media\" id=\"fs-id1169141373744\" data-alt=\"The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from 0 to 8. The y-axis runs from 0 to 8. The function has a starting point at (0, 0) and goes through the points (1, 2) and (4, 4).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_08_07_311_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from 0 to 8. The y-axis runs from 0 to 8. The function has a starting point at (0, 0) and goes through the points (1, 2) and (4, 4).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span>\\(\\left[0,\\infty \\right)\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169141373780\"><div data-type=\"problem\" id=\"fs-id1169148049774\"><p id=\"fs-id1169148049776\">\\(g\\left(x\\right)=3\\sqrt{x}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169145573813\"><div data-type=\"problem\" id=\"fs-id1169145573815\"><p id=\"fs-id1169145573817\">\\(f\\left(x\\right)=\\sqrt{3-x}\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169145748017\"><p id=\"fs-id1169145748019\"><span class=\"token\">\u24d0<\/span> domain: \\(\\left(\\text{\u2212}\\infty ,3\\right]\\)<\/p><div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d1<\/span><div data-type=\"newline\"><br><\/div> <span data-type=\"media\" id=\"fs-id1169145748049\" data-alt=\"The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 6 to 4. The y-axis runs from 0 to 8. The function has a starting point at (3, 0) and goes through the points (2, 1), (negative 1, 2), and (negative 6, 3).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_08_07_313_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 6 to 4. The y-axis runs from 0 to 8. The function has a starting point at (3, 0) and goes through the points (2, 1), (negative 1, 2), and (negative 6, 3).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span>\\(\\left[0,\\infty \\right)\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169143305900\"><div data-type=\"problem\" id=\"fs-id1169143305902\"><p id=\"fs-id1169143305905\">\\(f\\left(x\\right)=\\sqrt{4-x}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169143519080\"><div data-type=\"problem\" id=\"fs-id1169143519082\"><p id=\"fs-id1169143519085\">\\(g\\left(x\\right)=\\text{\u2212}\\sqrt{x}\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169143519108\"><p id=\"fs-id1169143519110\"><span class=\"token\">\u24d0<\/span> domain: \\(\\left[0,\\infty \\right)\\)<\/p><div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d1<\/span><div data-type=\"newline\"><br><\/div> <span data-type=\"media\" id=\"fs-id1169147797041\" data-alt=\"The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from 0 to 8. The y-axis runs from negative 8 to 0. The function has a starting point at (0, 0) and goes through the points (1, negative 1) and (4, negative 2).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_08_07_315_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from 0 to 8. The y-axis runs from negative 8 to 0. The function has a starting point at (0, 0) and goes through the points (1, negative 1) and (4, negative 2).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span>\\(\\left(\\text{\u2212}\\infty ,0\\right]\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169147797078\"><div data-type=\"problem\" id=\"fs-id1169147797080\"><p id=\"fs-id1169147797082\">\\(g\\left(x\\right)=\\text{\u2212}\\sqrt{x}+1\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169145977421\"><div data-type=\"problem\" id=\"fs-id1169145977423\"><p id=\"fs-id1169145977426\">\\(f\\left(x\\right)=\\sqrt[3]{x+1}\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169145977454\"><p id=\"fs-id1169145977456\"><span class=\"token\">\u24d0<\/span> domain: \\(\\left(\\text{\u2212}\\infty ,\\infty \\right)\\)<\/p><div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d1<\/span><div data-type=\"newline\"><br><\/div> <span data-type=\"media\" id=\"fs-id1169145977630\" data-alt=\"The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The function has a center point at (negative 1, 0) and goes through the points (negative 2, negative 1) and (0, 1).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_08_07_317_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The function has a center point at (negative 1, 0) and goes through the points (negative 2, negative 1) and (0, 1).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span>\\(\\left(\\text{\u2212}\\infty ,\\infty \\right)\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169145977667\"><div data-type=\"problem\" id=\"fs-id1169145977670\"><p id=\"fs-id1169145977672\">\\(f\\left(x\\right)=\\sqrt[3]{x-1}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169148062987\"><div data-type=\"problem\" id=\"fs-id1169148062989\"><p id=\"fs-id1169148062991\">\\(g\\left(x\\right)=\\sqrt[3]{x+2}\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169148063020\"><p id=\"fs-id1169148063022\"><span class=\"token\">\u24d0<\/span> domain: \\(\\left(\\text{\u2212}\\infty ,\\infty \\right)\\)<\/p><div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d1<\/span><div data-type=\"newline\"><br><\/div> <span data-type=\"media\" id=\"fs-id1169147720433\" data-alt=\"The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The function has a center point at (negative 4, 0) and goes through the points (negative 3, negative 1) and (negative 1, 1).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_08_07_319_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The function has a center point at (negative 4, 0) and goes through the points (negative 3, negative 1) and (negative 1, 1).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span>\\(\\left(\\text{\u2212}\\infty ,\\infty \\right)\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169147720471\"><div data-type=\"problem\" id=\"fs-id1169147720473\"><p id=\"fs-id1169147720475\">\\(g\\left(x\\right)=\\sqrt[3]{x-2}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169143316905\"><div data-type=\"problem\" id=\"fs-id1169143316907\"><p id=\"fs-id1169143316909\">\\(f\\left(x\\right)=\\sqrt[3]{x}+3\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169143316937\"><p id=\"fs-id1169143316939\"><span class=\"token\">\u24d0<\/span> domain: \\(\\left(\\text{\u2212}\\infty ,\\infty \\right)\\)<\/p><div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d1<\/span><div data-type=\"newline\"><br><\/div> <span data-type=\"media\" id=\"fs-id1169143316969\" data-alt=\"The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 2 to 6. The function has a center point at (0, 3) and goes through the points (negative 1, 2) and (1, 4).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_08_07_321_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 2 to 6. The function has a center point at (0, 3) and goes through the points (negative 1, 2) and (1, 4).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span>\\(\\left(\\text{\u2212}\\infty ,\\infty \\right)\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169141376312\"><div data-type=\"problem\" id=\"fs-id1169141376314\"><p id=\"fs-id1169141376316\">\\(f\\left(x\\right)=\\sqrt[3]{x}-3\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169145579077\"><div data-type=\"problem\" id=\"fs-id1169145579079\"><p id=\"fs-id1169145579081\">\\(g\\left(x\\right)=\\sqrt[3]{x}\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169145579105\"><p id=\"fs-id1169145579107\"><span class=\"token\">\u24d0<\/span> domain: \\(\\left(\\text{\u2212}\\infty ,\\infty \\right)\\)<\/p><div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d1<\/span><div data-type=\"newline\"><br><\/div> <span data-type=\"media\" id=\"fs-id1169145579137\" data-alt=\"The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The function has a center point at (0, 0) and goes through the points (1, 1) and (negative 1, negative 1).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_08_07_323_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The function has a center point at (0, 0) and goes through the points (1, 1) and (negative 1, negative 1).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span>\\(\\left(\\text{\u2212}\\infty ,\\infty \\right)\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169147987528\"><div data-type=\"problem\" id=\"fs-id1169147987530\"><p id=\"fs-id1169147987532\">\\(g\\left(x\\right)=\\text{\u2212}\\sqrt[3]{x}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169148063131\"><div data-type=\"problem\" id=\"fs-id1169148063133\"><p id=\"fs-id1169148063135\">\\(f\\left(x\\right)=2\\sqrt[3]{x}\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169148063160\"><p id=\"fs-id1169148063163\"><span class=\"token\">\u24d0<\/span> domain: \\(\\left(\\text{\u2212}\\infty ,\\infty \\right)\\)<\/p><div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d1<\/span><div data-type=\"newline\"><br><\/div> <span data-type=\"media\" id=\"fs-id1169148063192\" data-alt=\"The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The function has a center point at (0, 0) and goes through the points (1, 2) and (negative 1, negative 2).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_08_07_325_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The function has a center point at (0, 0) and goes through the points (1, 2) and (negative 1, negative 2).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span>\\(\\left(\\text{\u2212}\\infty ,\\infty \\right)\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169147725430\"><div data-type=\"problem\" id=\"fs-id1169147725432\"><p id=\"fs-id1169147725434\">\\(f\\left(x\\right)=-2\\sqrt[3]{x}\\)<\/p><\/div><\/div><\/div><div class=\"writing\" data-depth=\"2\" id=\"fs-id1169148053100\"><h4 data-type=\"title\">Writing Exercises<\/h4><div data-type=\"exercise\" id=\"fs-id1169148053107\"><div data-type=\"problem\" id=\"fs-id1169148053109\"><p id=\"fs-id1169148053111\">Explain how to find the domain of a fourth root function.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169148053115\"><p id=\"fs-id1169148053117\">Answers will vary.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169148053123\"><div data-type=\"problem\" id=\"fs-id1169148053125\"><p id=\"fs-id1169148053127\">Explain how to find the domain of a fifth root function.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169148053139\"><div data-type=\"problem\" id=\"fs-id1169148053141\"><p id=\"fs-id1169148053143\">Explain why \\(y=\\sqrt[3]{x}\\) is a function.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1169148053161\"><p id=\"fs-id1169148053163\">Answers will vary.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1169148053168\"><div data-type=\"problem\" id=\"fs-id1169148053171\"><p id=\"fs-id1169148053173\">Explain why the process of finding the domain of a radical function with an even index is different from the process when the index is odd.<\/p><\/div><\/div><\/div><div class=\"bc-section section\" data-depth=\"2\" id=\"fs-id1169148053187\"><h4 data-type=\"title\">Self Check<\/h4><p id=\"fs-id1169148053192\"><span class=\"token\">\u24d0<\/span> After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.<\/p><span data-type=\"media\" id=\"fs-id1169143519206\" data-alt=\"The table has 4 columns and 4 rows. The first row is a header row with the headers \u201cI can\u2026\u201d, \u201cConfidently\u201d, \u201cWith some help.\u201d, and \u201cNo \u2013 I don\u2019t get it!\u201d. The first column contains the phrases \u201cevaluate a radical function\u201d, \u201cfind the domain of a radical function\u201d, and \u201cgraph a radical function\u201d. The other columns are left blank so the learner can indicate their level of understanding.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_08_07_201_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The table has 4 columns and 4 rows. The first row is a header row with the headers \u201cI can\u2026\u201d, \u201cConfidently\u201d, \u201cWith some help.\u201d, and \u201cNo \u2013 I don\u2019t get it!\u201d. The first column contains the phrases \u201cevaluate a radical function\u201d, \u201cfind the domain of a radical function\u201d, and \u201cgraph a radical function\u201d. The other columns are left blank so the learner can indicate their level of understanding.\"><\/span><p id=\"fs-id1169148053206\"><span class=\"token\">\u24d1<\/span> What does this checklist tell you about your mastery of this section? What steps will you take to improve?<\/p><\/div><\/div><div data-type=\"glossary\" class=\"textbox shaded\"><h3 data-type=\"glossary-title\">Glossary<\/h3><dl id=\"fs-id1169143519223\"><dt>radical function<\/dt><dd id=\"fs-id1169143519229\">A radical function is a function that is defined by a radical expression.<\/dd><\/dl><\/div>\n","rendered":"<div class=\"textbox textbox--learning-objectives\">\n<h3 itemprop=\"educationalUse\">Learning Objectives<\/h3>\n<p>By the end of this section, you will be able to: <\/p>\n<ul>\n<li>Evaluate a radical function<\/li>\n<li>Find the domain of a radical function<\/li>\n<li>Graph radical functions<\/li>\n<\/ul>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1169145658240\" class=\"be-prepared\">\n<p id=\"fs-id1169147769294\">Before you get started, take this readiness quiz.<\/p>\n<ol id=\"fs-id1169143746917\" type=\"1\">\n<li>Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a00c4e769f9d507a8ca91e607aa3fc28_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#45;&#50;&#120;&#92;&#103;&#101;&#32;&#48;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"85\" style=\"vertical-align: -3px;\" \/>\n<div data-type=\"newline\"><\/div>\n<p> If you missed this problem, review <a href=\"\/contents\/27141d73-3006-49fa-98eb-5744b312aea7#fs-id1167835419716\" class=\"autogenerated-content\">(Figure)<\/a>.<\/li>\n<li>For <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8ccd2db587b10482d75fd78ceb048e20_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#51;&#120;&#45;&#52;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"115\" style=\"vertical-align: -4px;\" \/> evaluate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7246b632e2e1a992f0b1d12044e8e34f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"151\" style=\"vertical-align: -4px;\" \/>\n<div data-type=\"newline\"><\/div>\n<p> If you missed this problem, review <a href=\"\/contents\/5e548626-8f0f-496d-ab87-4f0358ca2fd3#fs-id1167836521479\" class=\"autogenerated-content\">(Figure)<\/a>.<\/li>\n<li>Graph <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b2d25193160b4d885fd9c76379754ebc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#120;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"90\" style=\"vertical-align: -4px;\" \/> State the domain and range of the function in interval notation.\n<div data-type=\"newline\"><\/div>\n<p> If you missed this problem, review <a href=\"\/contents\/da9d6ce0-a078-4ca2-97af-8cb374f040f5#fs-id1167829930477\" class=\"autogenerated-content\">(Figure)<\/a>.<\/li>\n<\/ol>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1169145644347\">\n<h3 data-type=\"title\">Evaluate a Radical Function<\/h3>\n<p id=\"fs-id1169147750184\">In this section we will extend our previous work with functions to include radicals. If a function is defined by a radical expression, we call it a <span data-type=\"term\">radical function<\/span>.<\/p>\n<p id=\"fs-id1169143574637\">The square root function is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7037f13d20c67547fd07ad5c2fd2e732_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#91;&#93;&#123;&#120;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"85\" style=\"vertical-align: -4px;\" \/><\/p>\n<p id=\"fs-id1169145658807\">The cube root function is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8a0afb0d325679df929272e77bb872e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#91;&#51;&#93;&#123;&#120;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"91\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"note\" id=\"fs-id1169147959288\">\n<div data-type=\"title\">Radical Function<\/div>\n<p id=\"fs-id1169145732376\">A <strong data-effect=\"bold\">radical function<\/strong> is a function that is defined by a radical expression.<\/p>\n<\/div>\n<p id=\"fs-id1169145640177\">To evaluate a radical function, we find the value of <em data-effect=\"italics\">f<\/em>(<em data-effect=\"italics\">x<\/em>) for a given value of <em data-effect=\"italics\">x<\/em> just as we did in our previous work with functions.<\/p>\n<div data-type=\"example\" id=\"fs-id1169147834542\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1169148054498\">\n<div data-type=\"problem\" id=\"fs-id1169147763493\">\n<p id=\"fs-id1169147767920\">For the function <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-827be1d378545c69be1ffa241becd5d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#120;&#45;&#49;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"129\" style=\"vertical-align: -4px;\" \/> find <span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-00e628545709308df2fad3ec5e77a716_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"35\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0ccfd7ec77d7d595dca58ab727de8ffd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"57\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169147759005\">\n<p id=\"fs-id1169147864033\"><span class=\"token\">\u24d0<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ded16592cc0b716016e97ba013770471_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#51;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#120;&#45;&#49;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#84;&#111;&#32;&#101;&#118;&#97;&#108;&#117;&#97;&#116;&#101;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#117;&#98;&#115;&#116;&#105;&#116;&#117;&#116;&#101;&#32;&#53;&#32;&#102;&#111;&#114;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#46;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#51;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#115;&#113;&#114;&#116;&#123;&#50;&middot;&#53;&#45;&#49;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#105;&#109;&#112;&#108;&#105;&#102;&#121;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#51;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#115;&#113;&#114;&#116;&#123;&#57;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#84;&#97;&#107;&#101;&#32;&#116;&#104;&#101;&#32;&#115;&#113;&#117;&#97;&#114;&#101;&#32;&#114;&#111;&#111;&#116;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#51;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#51;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"532\" style=\"vertical-align: -37px;\" \/><\/p>\n<p id=\"fs-id1169143231118\"><span class=\"token\">\u24d1<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8be1f25abeaa0870087e1c31d7f2c2e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#120;&#45;&#49;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#84;&#111;&#32;&#101;&#118;&#97;&#108;&#117;&#97;&#116;&#101;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#117;&#98;&#115;&#116;&#105;&#116;&#117;&#116;&#101;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#45;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#102;&#111;&#114;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#46;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#49;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#105;&#109;&#112;&#108;&#105;&#102;&#121;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#115;&#113;&#114;&#116;&#123;&#45;&#53;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"580\" style=\"vertical-align: -27px;\" \/><\/p>\n<p id=\"fs-id1169148229400\">Since the square root of a negative number is not a real number, the function does not have a value at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-86f872935a384592f05d5fdc077a0a0f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#50;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"61\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1169145620857\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1169147879034\">\n<div data-type=\"problem\" id=\"fs-id1169148248313\">\n<p id=\"fs-id1169148063652\">For the function <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-1e5110b687b582bb318ae826351853ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#51;&#120;&#45;&#50;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"129\" style=\"vertical-align: -4px;\" \/> find <span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-293254ff07d0ea3b3480491f90c1ce10_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"35\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-db4f958b4c4deacd90047ad0c954283a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"43\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169145498016\">\n<p><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-1c81c52d67bdfcba56c7ee66cebd5a4a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"69\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d1<\/span> no value at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8203ced39e0cdafefa708857c7ec2264_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1169147796778\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1169147765727\">\n<div data-type=\"problem\" id=\"fs-id1169147859022\">\n<p id=\"fs-id1169145988381\">For the function <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-9d7c7aff0dc58fbf2e3b64239ca3282d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#53;&#120;&#43;&#53;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"128\" style=\"vertical-align: -4px;\" \/> find <span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-49fcaf9fe488cacd08d464d30c0c480c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"34\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-509f3b07987f0f1e75e9db8e5bae79e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"55\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169145623485\">\n<p id=\"fs-id1169145586011\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f475ec9dee6ca52823167d484a81c598_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"66\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d1<\/span> no value at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-323b7bb2b4781d94070ede4656b35c82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"49\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169147987998\">We follow the same procedure to evaluate cube roots.<\/p>\n<div data-type=\"example\" id=\"fs-id1169145664723\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1169147820779\">\n<div data-type=\"problem\" id=\"fs-id1169147877799\">\n<p id=\"fs-id1169145715326\">For the function <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-4cea06fe770f3a3d2f983c8a4c701529_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#91;&#51;&#93;&#123;&#120;&#45;&#54;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"120\" style=\"vertical-align: -4px;\" \/> find <span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b1c4398b5feaa5dcee19dcf72dc7f459_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"43\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-82a8451ccbea9dd2f47b6b69e1586f07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"55\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169147745183\">\n<p id=\"fs-id1169148207457\"><span class=\"token\">\u24d0<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-1c10103ac13fc8180613d12cba978ef8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#115;&#113;&#114;&#116;&#91;&#51;&#93;&#123;&#120;&#45;&#54;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#84;&#111;&#32;&#101;&#118;&#97;&#108;&#117;&#97;&#116;&#101;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#117;&#98;&#115;&#116;&#105;&#116;&#117;&#116;&#101;&#32;&#49;&#52;&#32;&#102;&#111;&#114;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#46;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#115;&#113;&#114;&#116;&#91;&#51;&#93;&#123;&#49;&#52;&#45;&#54;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#105;&#109;&#112;&#108;&#105;&#102;&#121;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#115;&#113;&#114;&#116;&#91;&#51;&#93;&#123;&#56;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#84;&#97;&#107;&#101;&#32;&#116;&#104;&#101;&#32;&#99;&#117;&#98;&#101;&#32;&#114;&#111;&#111;&#116;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"510\" style=\"vertical-align: -37px;\" \/><\/p>\n<p id=\"fs-id1169143763234\"><span class=\"token\">\u24d1<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-cc9d48de65a2b1987695b64b7e395ff7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#115;&#113;&#114;&#116;&#91;&#51;&#93;&#123;&#120;&#45;&#54;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#84;&#111;&#32;&#101;&#118;&#97;&#108;&#117;&#97;&#116;&#101;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#117;&#98;&#115;&#116;&#105;&#116;&#117;&#116;&#101;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#45;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#102;&#111;&#114;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#46;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#115;&#113;&#114;&#116;&#91;&#51;&#93;&#123;&#45;&#50;&#45;&#54;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#105;&#109;&#112;&#108;&#105;&#102;&#121;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#115;&#113;&#114;&#116;&#91;&#51;&#93;&#123;&#45;&#56;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#84;&#97;&#107;&#101;&#32;&#116;&#104;&#101;&#32;&#99;&#117;&#98;&#101;&#32;&#114;&#111;&#111;&#116;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#45;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"524\" style=\"vertical-align: -37px;\" \/><\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1169143573107\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1169147843527\">\n<div data-type=\"problem\" id=\"fs-id1169145575010\">\n<p id=\"fs-id1169145714216\">For the function <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-712dddcf9b4ec96ff70d4a774a06cf21_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#91;&#51;&#93;&#123;&#51;&#120;&#45;&#52;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"129\" style=\"vertical-align: -4px;\" \/> find <span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-49fcaf9fe488cacd08d464d30c0c480c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"34\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-23c429bc610d1ce2cd5098e15cfa6122_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"42\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169145644143\">\n<p id=\"fs-id1169145779297\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-9937c3476d5a803e847d3404f0fdac10_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"66\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-69d1631a2396e936e9cbd22534f7b4f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"80\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1169147833350\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1169145733809\">\n<div data-type=\"problem\" id=\"fs-id1169147825232\">\n<p id=\"fs-id1169148229294\">For the function <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c1306072433483d0032b1b21b2ef0641_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#91;&#51;&#93;&#123;&#53;&#120;&#45;&#50;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"130\" style=\"vertical-align: -4px;\" \/> find <span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-adc2fe4535c765fcad10f3b4b4e1a8f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"35\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b726dcf8da225a0f0f445de9849b8c8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"57\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169147727895\">\n<p id=\"fs-id1169143550222\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-78a944d29636e5534b31a49a98fe8ab9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"67\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-08e5218fa9daf1c30543cda68304d2dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"96\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169148124976\">The next example has fourth roots.<\/p>\n<div data-type=\"example\" id=\"fs-id1169145667545\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1169145620381\">\n<div data-type=\"problem\" id=\"fs-id1169147806731\">\n<p id=\"fs-id1169145574634\">For the function <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e09a62148c445875073f2e367dbdcd0c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#91;&#52;&#93;&#123;&#53;&#120;&#45;&#52;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"130\" style=\"vertical-align: -4px;\" \/> find <span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c5ca7959d454ac362604a7c61a837ac7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"35\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-5771338d5c162029ea3707aebc22cd3d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"58\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169148233330\">\n<p id=\"fs-id1169148229060\"><span class=\"token\">\u24d0<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b6e9230438fe6dd4f6e6b84b7457fe02_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#51;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#115;&#113;&#114;&#116;&#91;&#52;&#93;&#123;&#53;&#120;&#45;&#52;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#84;&#111;&#32;&#101;&#118;&#97;&#108;&#117;&#97;&#116;&#101;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#117;&#98;&#115;&#116;&#105;&#116;&#117;&#116;&#101;&#32;&#52;&#32;&#102;&#111;&#114;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#46;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#51;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#115;&#113;&#114;&#116;&#91;&#52;&#93;&#123;&#53;&middot;&#52;&#45;&#52;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#105;&#109;&#112;&#108;&#105;&#102;&#121;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#51;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#115;&#113;&#114;&#116;&#91;&#52;&#93;&#123;&#49;&#54;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#84;&#97;&#107;&#101;&#32;&#116;&#104;&#101;&#32;&#102;&#111;&#117;&#114;&#116;&#104;&#32;&#114;&#111;&#111;&#116;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#51;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"541\" style=\"vertical-align: -37px;\" \/><\/p>\n<p id=\"fs-id1169147841823\"><span class=\"token\">\u24d1<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-fbd245c340120038156e48ffa5ded85f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#115;&#113;&#114;&#116;&#91;&#52;&#93;&#123;&#53;&#120;&#45;&#52;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#84;&#111;&#32;&#101;&#118;&#97;&#108;&#117;&#97;&#116;&#101;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#117;&#98;&#115;&#116;&#105;&#116;&#117;&#116;&#101;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#45;&#49;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#102;&#111;&#114;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#46;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#115;&#113;&#114;&#116;&#91;&#52;&#93;&#123;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#52;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#105;&#109;&#112;&#108;&#105;&#102;&#121;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#115;&#113;&#114;&#116;&#91;&#52;&#93;&#123;&#45;&#54;&#52;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"590\" style=\"vertical-align: -27px;\" \/><\/p>\n<p id=\"fs-id1169143638539\">Since the fourth root of a negative number is not a real number, the function does not have a value at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-af16f44d25db35987d9358fc47f09cd2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#49;&#50;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"70\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1169145946189\">\n<div data-type=\"problem\" id=\"fs-id1169147850137\">\n<p id=\"fs-id1169147847536\">For the function <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8d48c7d2bc13f15385d7b1e34ea04d0a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#91;&#52;&#93;&#123;&#51;&#120;&#43;&#52;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"130\" style=\"vertical-align: -4px;\" \/> find <span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c5ca7959d454ac362604a7c61a837ac7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"35\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ecce7991a775f49b2fd6e73ef9f01226_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"57\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169147806247\">\n<p id=\"fs-id1169147774929\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c21cb0b6ad785021d9f8bf12324dc394_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"68\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-025b08bb2b244219e5017a751a95a71c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"82\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1169147707374\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1169143317888\">\n<div data-type=\"problem\" id=\"fs-id1169147906250\">\n<p id=\"fs-id1169147843734\">For the function <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8259a05baa16929c356a61a9870c43d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#91;&#52;&#93;&#123;&#53;&#120;&#43;&#49;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"129\" style=\"vertical-align: -4px;\" \/> find <span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-6f41f437f1343307947071f7cf0c25f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"43\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-46e63ebcaf7174459b89e4ae8e8b393b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"42\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169147979561\">\n<p id=\"fs-id1169142122817\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-cfc7501eef1c9a7658120f06bc4c88d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"76\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-867cf3c185a06a901ec6d5d07aadd50b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"66\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1169147775047\">\n<h3 data-type=\"title\">Find the Domain of a Radical Function<\/h3>\n<p id=\"fs-id1169147824778\">To find the <span data-type=\"term\" class=\"no-emphasis\">domain<\/span> and <span data-type=\"term\" class=\"no-emphasis\">range<\/span> of radical functions, we use our properties of radicals. For a radical with an even index, we said the radicand had to be greater than or equal to zero as even roots of negative numbers are not real numbers. For an odd index, the radicand can be any real number. We restate the properties here for reference.<\/p>\n<div data-type=\"note\" id=\"fs-id1169148047556\">\n<div data-type=\"title\">Properties of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-1c6b7326bec5fc086e8335bb7e382f30_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#91;&#110;&#93;&#123;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"23\" style=\"vertical-align: -4px;\" \/><\/div>\n<p id=\"fs-id1169147835801\">When <em data-effect=\"italics\">n<\/em> is an <strong data-effect=\"bold\">even<\/strong> number and:<\/p>\n<ul id=\"fs-id1169147848685\" data-bullet-style=\"bullet\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f75133c2b77e2f59b82bc9d582b4e840_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#103;&#101;&#32;&#48;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"46\" style=\"vertical-align: -4px;\" \/> then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-1c6b7326bec5fc086e8335bb7e382f30_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#91;&#110;&#93;&#123;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"23\" style=\"vertical-align: -4px;\" \/> is a real number.<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-36c26ea6de309fb94494920502960413_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#60;&#48;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"46\" style=\"vertical-align: -4px;\" \/> then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-1c6b7326bec5fc086e8335bb7e382f30_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#91;&#110;&#93;&#123;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"23\" style=\"vertical-align: -4px;\" \/> is not a real number.<\/li>\n<\/ul>\n<p id=\"fs-id1169147763639\">When <em data-effect=\"italics\">n<\/em> is an <strong data-effect=\"bold\">odd<\/strong> number, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-1c6b7326bec5fc086e8335bb7e382f30_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#91;&#110;&#93;&#123;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"23\" style=\"vertical-align: -4px;\" \/> is a real number for all values of <em data-effect=\"italics\">a<\/em>.<\/p>\n<\/div>\n<p id=\"fs-id1169147865230\">So, to find the domain of a radical function with even index, we set the radicand to be greater than or equal to zero. For an odd index radical, the radicand can be any real number.<\/p>\n<div data-type=\"note\" id=\"fs-id1169147837500\">\n<div data-type=\"title\">Domain of a Radical Function<\/div>\n<p id=\"fs-id1169147745047\">When the <strong data-effect=\"bold\">index<\/strong> of the radical is <strong data-effect=\"bold\">even<\/strong>, the radicand must be greater than or equal to zero.<\/p>\n<p id=\"fs-id1169143550091\">When the <strong data-effect=\"bold\">index<\/strong> of the radical is <strong data-effect=\"bold\">odd<\/strong>, the radicand can be any real number.<\/p>\n<\/div>\n<div data-type=\"example\" id=\"fs-id1169145747305\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1169145730306\">\n<div data-type=\"problem\" id=\"fs-id1169147711453\">\n<p id=\"fs-id1169145620583\">Find the domain of the function, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ae876e44f5bcf56497f5bb6a25d6ca50_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#51;&#120;&#45;&#52;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"129\" style=\"vertical-align: -4px;\" \/> Write the domain in interval notation.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169145499784\">\n<p id=\"fs-id1169147809361\">Since the function, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7def2fd4cf5031bc2c7dcdec01eaa9bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#51;&#120;&#45;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"126\" style=\"vertical-align: -4px;\" \/> has a radical with an index of 2, which is even, we know the radicand must be greater than or equal to 0. We set the radicand to be greater than or equal to 0 and then solve to find the domain.<\/p>\n<p id=\"fs-id1169147826910\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-921d13a1329ddf4986d5a8e33780a93e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#51;&#120;&#45;&#52;&#38;&#32;&#92;&#103;&#101;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#111;&#108;&#118;&#101;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#51;&#120;&#38;&#32;&#92;&#103;&#101;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#52;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#120;&#38;&#32;&#92;&#103;&#101;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#51;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"62\" width=\"231\" style=\"vertical-align: -28px;\" \/><\/p>\n<p id=\"fs-id1169143577542\">The domain of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7def2fd4cf5031bc2c7dcdec01eaa9bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#51;&#120;&#45;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"126\" style=\"vertical-align: -4px;\" \/> is all values <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-11976e85d294bf4f9232ea3329cdb819_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#92;&#103;&#101;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"43\" style=\"vertical-align: -6px;\" \/> and we write it in interval notation as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-65f2df8100105ecc3c25bf00b6f7b7a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#51;&#125;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"56\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1169145520198\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1169145644630\">\n<div data-type=\"problem\" id=\"fs-id1169147959847\">\n<p id=\"fs-id1169148210160\">Find the domain of the function, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-3ffa98d8d5c46ba2d294c295b69e7ea8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#54;&#120;&#45;&#53;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"129\" style=\"vertical-align: -4px;\" \/> Write the domain in interval notation.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169148037760\">\n<p id=\"fs-id1169148251259\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-6bbdf310ed95236bb0e8a1e95a9189de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#54;&#125;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"47\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1169147909572\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1169145550678\">\n<div data-type=\"problem\" id=\"fs-id1169147860226\">\n<p id=\"fs-id1169148115867\">Find the domain of the function, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-32c188b5960774daa29b1172b3d723b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#52;&#45;&#53;&#120;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"129\" style=\"vertical-align: -4px;\" \/> Write the domain in interval notation.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169147838012\">\n<p id=\"fs-id1169147852288\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-fbf2475179d8d62a61ebd562ffd1bd67_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#44;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#93;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"46\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"example\" id=\"fs-id1169147764891\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1169143601638\">\n<div data-type=\"problem\" id=\"fs-id1169145574085\">\n<p id=\"fs-id1169145716676\">Find the domain of the function, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-6781cbc80b91883ecb1b52f93fc23274_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#125;&#123;&#120;&#45;&#49;&#125;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"111\" style=\"vertical-align: -12px;\" \/> Write the domain in interval notation.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169148248332\">\n<p id=\"fs-id1169147738757\">Since the function, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e8aaaf7ded6156ab643579fccb7d7f94_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#125;&#123;&#120;&#45;&#49;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"107\" style=\"vertical-align: -12px;\" \/> has a radical with an index of 2, which is even, we know the radicand must be greater than or equal to 0.<\/p>\n<p id=\"fs-id1169143330161\">The radicand cannot be zero since the numerator is not zero.<\/p>\n<p id=\"fs-id1169145608090\">For <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-4c28bcc62cbd7853092d1f2f877e5fcf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#125;&#123;&#120;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"26\" style=\"vertical-align: -7px;\" \/> to be greater than zero, the denominator must be positive since the numerator is positive. We know a positive divided by a positive is positive.<\/p>\n<p id=\"fs-id1169147731977\">We set <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-6ab3d6dd80f7ed27db3f9767839cc8c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#49;&#62;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"73\" style=\"vertical-align: -1px;\" \/> and solve.<\/p>\n<p id=\"fs-id1169143487387\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-9a96ed4f318e323fcee9e6f3767421d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#120;&#45;&#49;&#38;&#32;&#62;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#111;&#108;&#118;&#101;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#120;&#38;&#32;&#62;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#49;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"35\" width=\"222\" style=\"vertical-align: -12px;\" \/><\/p>\n<p id=\"fs-id1169145507872\">Also, since the radicand is a fraction, we must realize that the denominator cannot be zero.<\/p>\n<p id=\"fs-id1169147817212\">We solve <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-2a57ca6c48b6f646aeb64eb7f05e4840_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#49;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"73\" style=\"vertical-align: -1px;\" \/> to find the value that must be eliminated from the domain.<\/p>\n<p id=\"fs-id1169147758791\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-075c57b480de09723f930d7248d0fcc1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#120;&#45;&#49;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#111;&#108;&#118;&#101;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#120;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#49;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#111;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#92;&#110;&#101;&#32;&#49;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#110;&#32;&#116;&#104;&#101;&#32;&#100;&#111;&#109;&#97;&#105;&#110;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"404\" style=\"vertical-align: -15px;\" \/><\/p>\n<p id=\"fs-id1169143578779\">Putting this together we get the domain is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a4d9276cbc57460042be47a38f9e60d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#62;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" style=\"vertical-align: -1px;\" \/> and we write it as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-aa5fa4581591b8aab1c976a4b2d691a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"54\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1169145665511\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1169147777460\">\n<div data-type=\"problem\" id=\"fs-id1169148224616\">\n<p id=\"fs-id1169147875579\">Find the domain of the function, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-546b69e3de62a59b6172b505659edbcb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#120;&#43;&#51;&#125;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"112\" style=\"vertical-align: -12px;\" \/> Write the domain in interval notation.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169148101058\">\n<p id=\"fs-id1169147946981\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c4b4c62a0f4b8b806f67b5b2e234e710_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"60\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1169147802653\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1169147764968\">\n<div data-type=\"problem\" id=\"fs-id1169147965038\">\n<p id=\"fs-id1169142263113\">Find the domain of the function, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-4f3c0f86ba1fac364c82b216100e4bef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#120;&#45;&#53;&#125;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"112\" style=\"vertical-align: -12px;\" \/> Write the domain in interval notation.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169148211614\">\n<p id=\"fs-id1169145505677\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-142f88fb5277b03777a98d153da908e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"47\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169147962378\">The next example involves a cube root and so will require different thinking.<\/p>\n<div data-type=\"example\" id=\"fs-id1169147833926\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1169147768127\">\n<div data-type=\"problem\" id=\"fs-id1169145621716\">\n<p id=\"fs-id1169145580555\">Find the domain of the function, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-39777969a390d43ba0df6a5336262888_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#91;&#51;&#93;&#123;&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"138\" style=\"vertical-align: -4px;\" \/> Write the domain in interval notation.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169147700003\">\n<p id=\"fs-id1169147947059\">Since the function, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-efa4311db239c601216b356724f48314_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#91;&#51;&#93;&#123;&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"135\" style=\"vertical-align: -4px;\" \/> has a radical with an index of 3, which is odd, we know the radicand can be any real number. This tells us the domain is any real number. In interval notation, we write <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-5df92a2cc0a08c383e86c9bcbca032bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -4px;\" \/><\/p>\n<p id=\"fs-id1169147980456\">The domain of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-efa4311db239c601216b356724f48314_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#91;&#51;&#93;&#123;&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"135\" style=\"vertical-align: -4px;\" \/> is all real numbers and we write it in interval notation as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-5df92a2cc0a08c383e86c9bcbca032bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1169145733006\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1169143502868\">\n<div data-type=\"problem\" id=\"fs-id1169147707473\">\n<p id=\"fs-id1169147864365\">Find the domain of the function, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-08e1ee66bcff89953cb9f30039fe7105_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#91;&#51;&#93;&#123;&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"138\" style=\"vertical-align: -4px;\" \/> Write the domain in interval notation.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169147837932\">\n<p id=\"fs-id1169145620600\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-90eaa2f0f55290692476556ec134a082_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1169147827855\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1169148077672\">\n<div data-type=\"problem\" id=\"fs-id1169148116396\">\n<p id=\"fs-id1169145670713\">Find the domain of the function, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e143aff0a75e014012cd4860a97b0f98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#91;&#51;&#93;&#123;&#53;&#120;&#45;&#52;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"129\" style=\"vertical-align: -4px;\" \/> Write the domain in interval notation.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169147804280\">\n<p id=\"fs-id1169147837605\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-90eaa2f0f55290692476556ec134a082_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1169147772022\">\n<h3 data-type=\"title\">Graph Radical Functions<\/h3>\n<p id=\"fs-id1169148251663\">Before we graph any radical function, we first find the <span data-type=\"term\" class=\"no-emphasis\">domain<\/span> of the function. For the function, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-dfe0ffb5060d07bda34e7a001245823a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#120;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"90\" style=\"vertical-align: -4px;\" \/> the index is even, and so the radicand must be greater than or equal to 0.<\/p>\n<p id=\"fs-id1169145506488\">This tells us the domain is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-46bb299f47d94e1927057d14ab78801f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#92;&#103;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"43\" style=\"vertical-align: -3px;\" \/> and we write this in interval notation as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-271d90226a42bdb8da42b4a74ff029d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#48;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"51\" style=\"vertical-align: -5px;\" \/><\/p>\n<p id=\"fs-id1169142400725\">Previously we used point plotting to graph the function, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b2d25193160b4d885fd9c76379754ebc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#120;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"90\" style=\"vertical-align: -4px;\" \/> We chose <em data-effect=\"italics\">x<\/em>-values, substituted them in and then created a chart. Notice we chose points that are perfect squares in order to make taking the square root easier.<\/p>\n<p><span data-type=\"media\" id=\"fs-id1169148231243\" data-alt=\"The figure shows the square root function graph on the x y-coordinate plane. The x-axis of the plane runs from 0 to 7. The y-axis runs from 0 to 7. The function has a starting point at (0, 0) and goes through the points (1, 1) and (4, 2). A table is shown beside the graph with 3 columns and 5 rows. The first row is a header row with the expressions \u201cx\u201d, \u201cf (x) = square root of x\u201d, and \u201c(x, f (x))\u201d. The second row has the numbers 0, 0, and (0, 0). The third row has the numbers 1, 1, and (1, 1). The fourth row has the numbers 4, 2, and (4, 2). The fifth row has the numbers 9, 3, and (9, 3).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_08_07_001_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows the square root function graph on the x y-coordinate plane. The x-axis of the plane runs from 0 to 7. The y-axis runs from 0 to 7. The function has a starting point at (0, 0) and goes through the points (1, 1) and (4, 2). A table is shown beside the graph with 3 columns and 5 rows. The first row is a header row with the expressions \u201cx\u201d, \u201cf (x) = square root of x\u201d, and \u201c(x, f (x))\u201d. The second row has the numbers 0, 0, and (0, 0). The third row has the numbers 1, 1, and (1, 1). The fourth row has the numbers 4, 2, and (4, 2). The fifth row has the numbers 9, 3, and (9, 3).\" \/><\/span><\/p>\n<p id=\"fs-id1169147774393\">Once we see the graph, we can find the range of the function. The <em data-effect=\"italics\">y<\/em>-values of the function are greater than or equal to zero. The range then is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-271d90226a42bdb8da42b4a74ff029d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#48;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"51\" style=\"vertical-align: -5px;\" \/><\/p>\n<div data-type=\"example\" id=\"fs-id1169148132081\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1169148072142\">\n<div data-type=\"problem\" id=\"fs-id1169147830798\">\n<p id=\"fs-id1169145775018\">For the function <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c38a8710defa56e3c4dcc1e510ed50a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#120;&#43;&#51;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"121\" style=\"vertical-align: -4px;\" \/><\/p>\n<p id=\"fs-id1169145735236\"><span class=\"token\">\u24d0<\/span> find the domain <span class=\"token\">\u24d1<\/span> graph the function <span class=\"token\">\u24d2<\/span> use the graph to determine the range.<\/p>\n<\/div>\n<div data-type=\"solution\">\n<p id=\"fs-id1169147959625\"><span class=\"token\">\u24d0<\/span> Since the radical has index 2, we know the radicand must be greater than or equal to zero. If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d855b310a7eea8c67f4667245f13ef02_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#51;&#92;&#103;&#101;&#32;&#48;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"77\" style=\"vertical-align: -4px;\" \/> then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d01f5d1821a5287a168bb52ae2ac416c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#92;&#103;&#101;&#32;&#45;&#51;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"61\" style=\"vertical-align: -3px;\" \/> This tells us the domain is all values <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-dfc84780b14328431bcc372ff904772d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#92;&#103;&#101;&#32;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"57\" style=\"vertical-align: -3px;\" \/> and written in interval notation as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a24cb4ba3a90ca736926975b382407e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#45;&#51;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -5px;\" \/><\/p>\n<p id=\"fs-id1169147787156\"><span class=\"token\">\u24d1<\/span> To graph the function, we choose points in the interval <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-32c7c1f6f66ad1f9bbb95d35f2c1b9f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#45;&#51;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"57\" style=\"vertical-align: -5px;\" \/> that will also give us a radicand which will be easy to take the square root.<\/p>\n<p><span data-type=\"media\" id=\"fs-id1169147716047\" data-alt=\"The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 3 to 3. The y-axis runs from 0 to 7. The function has a starting point at (negative 3, 0) and goes through the points (negative 2, 1) and (1, 2). A table is shown beside the graph with 3 columns and 5 rows. The first row is a header row with the expressions \u201cx\u201d, \u201cf (x) = square root of the quantity x plus 3\u201d, and \u201c(x, f (x))\u201d. The second row has the numbers negative 3, 0, and (negative 3, 0). The third row has the numbers negative 2, 1, and (negative 2, 1). The fourth row has the numbers 1, 2, and (1, 2). The fifth row has the numbers 6, 3, and (6, 3).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_08_07_002_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 3 to 3. The y-axis runs from 0 to 7. The function has a starting point at (negative 3, 0) and goes through the points (negative 2, 1) and (1, 2). A table is shown beside the graph with 3 columns and 5 rows. The first row is a header row with the expressions \u201cx\u201d, \u201cf (x) = square root of the quantity x plus 3\u201d, and \u201c(x, f (x))\u201d. The second row has the numbers negative 3, 0, and (negative 3, 0). The third row has the numbers negative 2, 1, and (negative 2, 1). The fourth row has the numbers 1, 2, and (1, 2). The fifth row has the numbers 6, 3, and (6, 3).\" \/><\/span><\/p>\n<p id=\"fs-id1169147708185\"><span class=\"token\">\u24d2<\/span> Looking at the graph, we see the <em data-effect=\"italics\">y<\/em>-values of the function are greater than or equal to zero. The range then is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-271d90226a42bdb8da42b4a74ff029d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#48;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"51\" style=\"vertical-align: -5px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1169137906940\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1169147826840\">\n<div data-type=\"problem\" id=\"fs-id1169148069963\">\n<p id=\"fs-id1169147738653\">For the function <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8430f42cc4009f71f13f52805a4bce60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#120;&#43;&#50;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"121\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d0<\/span> find the domain <span class=\"token\">\u24d1<\/span> graph the function <span class=\"token\">\u24d2<\/span> use the graph to determine the range.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169147834274\">\n<p id=\"fs-id1169145696314\"><span class=\"token\">\u24d0<\/span> domain: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-58cba6b887275185a1fe142174f2bd42_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#45;&#50;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"57\" style=\"vertical-align: -5px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d1<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span data-type=\"media\" id=\"fs-id1169145660319\" data-alt=\"The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 2 to 6. The y-axis runs from 0 to 8. The function has a starting point at (negative 2, 0) and goes through the points (negative 1, 1) and (2, 2).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_08_07_301_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 2 to 6. The y-axis runs from 0 to 8. The function has a starting point at (negative 2, 0) and goes through the points (negative 1, 1) and (2, 2).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span> range: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-2640870d7533edf8778f6e64ee0db9c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#48;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"44\" style=\"vertical-align: -5px;\" \/><\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1169145735224\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1169145731036\">\n<div data-type=\"problem\" id=\"fs-id1169147774570\">\n<p id=\"fs-id1169147836064\">For the function <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-9122eb6639d2e30fe1d399f32e7ccbd4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#120;&#45;&#50;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"121\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d0<\/span> find the domain <span class=\"token\">\u24d1<\/span> graph the function <span class=\"token\">\u24d2<\/span> use the graph to determine the range.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169145670796\">\n<p id=\"fs-id1169147906599\"><span class=\"token\">\u24d0<\/span> domain: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8eaeb3bff1145b627e5b8f6ec4e7bb43_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#50;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"44\" style=\"vertical-align: -5px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d1<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span data-type=\"media\" id=\"fs-id1169145969952\" data-alt=\"The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from 0 to 8. The y-axis runs from 0 to 6. The function has a starting point at (2, 0) and goes through the points (3, 1) and (6, 2).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_08_07_302_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from 0 to 8. The y-axis runs from 0 to 6. The function has a starting point at (2, 0) and goes through the points (3, 1) and (6, 2).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span> range: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-2640870d7533edf8778f6e64ee0db9c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#48;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"44\" style=\"vertical-align: -5px;\" \/><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169147759371\">In our previous work graphing functions, we graphed <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-3834cfa0dbc9b6c213a1fd470f6e15fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#123;&#120;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"78\" style=\"vertical-align: -4px;\" \/> but we did not graph the function <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8a0afb0d325679df929272e77bb872e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#91;&#51;&#93;&#123;&#120;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"91\" style=\"vertical-align: -4px;\" \/> We will do this now in the next example.<\/p>\n<div data-type=\"example\" id=\"fs-id1169147876087\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1169147708819\">\n<div data-type=\"problem\" id=\"fs-id1169145844089\">\n<p id=\"fs-id1169148237468\">For the function <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b2ca38a98c49f0b2264a6dbc2e51f138_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#91;&#51;&#93;&#123;&#120;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"91\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d0<\/span> find the domain <span class=\"token\">\u24d1<\/span> graph the function <span class=\"token\">\u24d2<\/span> use the graph to determine the range.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169147808469\">\n<p id=\"fs-id1169145643316\"><span class=\"token\">\u24d0<\/span> Since the radical has index 3, we know the radicand can be any real number. This tells us the domain is all real numbers and written in interval notation as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-90eaa2f0f55290692476556ec134a082_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/p>\n<p id=\"fs-id1169148054588\"><span class=\"token\">\u24d1<\/span> To graph the function, we choose points in the interval <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-90eaa2f0f55290692476556ec134a082_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"56\" style=\"vertical-align: -4px;\" \/> that will also give us a radicand which will be easy to take the cube root.<\/p>\n<p><span data-type=\"media\" id=\"fs-id1169147732107\" data-alt=\"The figure shows the cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The function has a center point at (0, 0) and goes through the points (1, 1), (negative 1, negative 1), (8, 2), and (negative 8, negative 2). A table is shown beside the graph with 3 columns and 6 rows. The first row is a header row with the expressions \u201cx\u201d, \u201cf (x) = cube root of x\u201d, and \u201c(x, f (x))\u201d. The second row has the numbers negative 8, negative 2, and (negative 8, negative 2). The third row has the numbers negative 1, negative 1, and (negative 1, negative 1). The fourth row has the numbers 0, 0, and (0, 0). The fifth row has the numbers 1, 1, and (1, 1). The sixth row has the numbers 8, 2, and (8, 2).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_08_07_003_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows the cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The function has a center point at (0, 0) and goes through the points (1, 1), (negative 1, negative 1), (8, 2), and (negative 8, negative 2). A table is shown beside the graph with 3 columns and 6 rows. The first row is a header row with the expressions \u201cx\u201d, \u201cf (x) = cube root of x\u201d, and \u201c(x, f (x))\u201d. The second row has the numbers negative 8, negative 2, and (negative 8, negative 2). The third row has the numbers negative 1, negative 1, and (negative 1, negative 1). The fourth row has the numbers 0, 0, and (0, 0). The fifth row has the numbers 1, 1, and (1, 1). The sixth row has the numbers 8, 2, and (8, 2).\" \/><\/span><\/p>\n<p id=\"fs-id1169147846342\"><span class=\"token\">\u24d2<\/span> Looking at the graph, we see the <em data-effect=\"italics\">y<\/em>-values of the function are all real numbers. The range then is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-5df92a2cc0a08c383e86c9bcbca032bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1169147741965\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1169147963259\">\n<div data-type=\"problem\" id=\"fs-id1169145924994\">\n<p id=\"fs-id1169145924996\">For the function <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-366d042cbbadc5c002a5f38c20b056fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#115;&#113;&#114;&#116;&#91;&#51;&#93;&#123;&#120;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"91\" style=\"vertical-align: -4px;\" \/><\/p>\n<p id=\"fs-id1169147831008\"><span class=\"token\">\u24d0<\/span> find the domain <span class=\"token\">\u24d1<\/span> graph the function <span class=\"token\">\u24d2<\/span> use the graph to determine the range.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169141300257\">\n<p id=\"fs-id1169143448553\"><span class=\"token\">\u24d0<\/span> domain: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-50f486b07fc79c69768e3c97fe65e693_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#40;&#125;&#45;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"70\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d1<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span data-type=\"media\" id=\"fs-id1169142133180\" data-alt=\"The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 2 to 2. The y-axis runs from negative 2 to 2. The function has a center point at (0, 0) and goes through the points (1, negative 1) and (negative 1, 1).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_08_07_303_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 2 to 2. The y-axis runs from negative 2 to 2. The function has a center point at (0, 0) and goes through the points (1, negative 1) and (negative 1, 1).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span> range: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-50f486b07fc79c69768e3c97fe65e693_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#40;&#125;&#45;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"70\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1169147747631\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1169147868760\">\n<div data-type=\"problem\" id=\"fs-id1169147868762\">\n<p id=\"fs-id1169147877505\">For the function <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d9b9dbcc90588714e95ffb0ed1bfd9e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#91;&#51;&#93;&#123;&#120;&#45;&#50;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"122\" style=\"vertical-align: -4px;\" \/><\/p>\n<p id=\"fs-id1169142417273\"><span class=\"token\">\u24d0<\/span> find the domain <span class=\"token\">\u24d1<\/span> graph the function <span class=\"token\">\u24d2<\/span> use the graph to determine the range.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169147983988\">\n<p id=\"fs-id1169147983990\"><span class=\"token\">\u24d0<\/span> domain: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-50f486b07fc79c69768e3c97fe65e693_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#40;&#125;&#45;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"70\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d1<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span data-type=\"media\" id=\"fs-id1169148076410\" data-alt=\"The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 1 to 5. The y-axis runs from negative 3 to 3. The function has a center point at (2, 0) and goes through the points (1, negative 1) and (3, 2).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_08_07_304_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 1 to 5. The y-axis runs from negative 3 to 3. The function has a center point at (2, 0) and goes through the points (1, negative 1) and (3, 2).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span> range: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-50f486b07fc79c69768e3c97fe65e693_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#40;&#125;&#45;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"70\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1169147978659\" class=\"media-2\">\n<p id=\"fs-id1169148126317\">Access these online resources for additional instruction and practice with radical functions.<\/p>\n<ul id=\"fs-id1169147948111\" data-display=\"block\">\n<li><a href=\"https:\/\/openstax.org\/l\/37RadFuncDom1\">Domain of a Radical Function<\/a><\/li>\n<li><a href=\"https:\/\/openstax.org\/l\/37RadFuncDom2\">Domain of a Radical Function 2<\/a><\/li>\n<li><a href=\"https:\/\/openstax.org\/l\/37RadFuncDom3\">Finding Domain of a Radical Function<\/a><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<div class=\"textbox\" data-depth=\"1\" id=\"fs-id1169147743296\">\n<h3 data-type=\"title\">Key Concepts<\/h3>\n<ul id=\"fs-id1169145717081\" data-bullet-style=\"bullet\">\n<li><strong data-effect=\"bold\">Properties of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-1c6b7326bec5fc086e8335bb7e382f30_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#91;&#110;&#93;&#123;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"23\" style=\"vertical-align: -4px;\" \/><\/strong>\n<ul id=\"fs-id1169141036816\" data-bullet-style=\"bullet\">\n<li>When <em data-effect=\"italics\">n<\/em> is an <strong data-effect=\"bold\">even<\/strong> number and:\n<div data-type=\"newline\"><\/div>\n<p> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f75133c2b77e2f59b82bc9d582b4e840_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#103;&#101;&#32;&#48;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"46\" style=\"vertical-align: -4px;\" \/> then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-1c6b7326bec5fc086e8335bb7e382f30_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#91;&#110;&#93;&#123;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"23\" style=\"vertical-align: -4px;\" \/> is a real number.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-36c26ea6de309fb94494920502960413_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#60;&#48;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"46\" style=\"vertical-align: -4px;\" \/> then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-1c6b7326bec5fc086e8335bb7e382f30_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#91;&#110;&#93;&#123;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"23\" style=\"vertical-align: -4px;\" \/> is not a real number.<\/li>\n<li>When <em data-effect=\"italics\">n<\/em> is an <strong data-effect=\"bold\">odd<\/strong> number, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-1c6b7326bec5fc086e8335bb7e382f30_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#91;&#110;&#93;&#123;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"23\" style=\"vertical-align: -4px;\" \/> is a real number for all values of <em data-effect=\"italics\">a<\/em>.<\/li>\n<\/ul>\n<\/li>\n<li><strong data-effect=\"bold\">Domain of a Radical Function<\/strong>\n<ul id=\"fs-id1169145645013\" data-bullet-style=\"bullet\">\n<li>When the <strong data-effect=\"bold\">index<\/strong> of the radical is <strong data-effect=\"bold\">even<\/strong>, the radicand must be greater than or equal to zero.<\/li>\n<li>When the <strong data-effect=\"bold\">index<\/strong> of the radical is <strong data-effect=\"bold\">odd<\/strong>, the radicand can be any real number.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/div>\n<div class=\"textbox\" data-depth=\"1\" id=\"fs-id1169148097720\">\n<div class=\"practice-perfect\" data-depth=\"2\" id=\"fs-id1169148231171\">\n<h4 data-type=\"title\">Practice Makes Perfect<\/h4>\n<p id=\"fs-id1169148101448\"><strong data-effect=\"bold\">Evaluate a Radical Function<\/strong><\/p>\n<p id=\"fs-id1169148209532\">In the following exercises, evaluate each function.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1169147743159\">\n<div data-type=\"problem\" id=\"fs-id1169145716402\">\n<p id=\"fs-id1169145716404\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d1a6f4fa76acb3f1949388c80915a73a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#52;&#120;&#45;&#52;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"129\" style=\"vertical-align: -4px;\" \/> find<\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-00e628545709308df2fad3ec5e77a716_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"35\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-db4f958b4c4deacd90047ad0c954283a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"43\" style=\"vertical-align: -4px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1169147800145\">\n<p id=\"fs-id1169142281310\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a44dcaf7033eff5d97891fb791fbce6c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"69\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d1<\/span> no value at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8203ced39e0cdafefa708857c7ec2264_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169142480106\">\n<div data-type=\"problem\" id=\"fs-id1169148101052\">\n<p id=\"fs-id1169148101054\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-4daa4124d8000c3e797986dc3efbe45e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#54;&#120;&#45;&#53;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"129\" style=\"vertical-align: -4px;\" \/> find<\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-00e628545709308df2fad3ec5e77a716_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"35\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ecce7991a775f49b2fd6e73ef9f01226_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"57\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169148207439\">\n<div data-type=\"problem\" id=\"fs-id1169147804241\">\n<p id=\"fs-id1169145620467\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b9a317b4d77475614a3dfa9395e555ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#54;&#120;&#43;&#49;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"128\" style=\"vertical-align: -4px;\" \/> find<\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-49fcaf9fe488cacd08d464d30c0c480c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"34\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a1f3b88e0114b15ff8e15a06a90a16c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"42\" style=\"vertical-align: -4px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1169145507838\">\n<p id=\"fs-id1169143580099\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f475ec9dee6ca52823167d484a81c598_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"66\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0133f4fd999be119d5d8fc15634bd751_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"67\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169147909782\">\n<div data-type=\"problem\" id=\"fs-id1169147865255\">\n<p id=\"fs-id1169147865257\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c2500b5b11ea080db4035816c155a404_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#51;&#120;&#43;&#49;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"128\" style=\"vertical-align: -4px;\" \/> find<\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-6cfbd3ae14c544c46b05ffbdd1f16f77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"34\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c6d2a15d706df77c40ce93f9502f3bd8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"42\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169145730224\">\n<div data-type=\"problem\" id=\"fs-id1169147758640\">\n<p id=\"fs-id1169147758642\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-fff8f806a8ef395c6964be61de4f4a7c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#51;&#45;&#50;&#120;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"133\" style=\"vertical-align: -4px;\" \/> find<\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0b961782c20464f4b584b9caa42b24ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8cd9e6950bff2bf55bcde1181b83b148_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"69\" style=\"vertical-align: -4px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1169148235035\">\n<p id=\"fs-id1169145505941\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-cbaf8ed1442cc698f40a357cca595b0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"71\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b22269bba3dc8f6a23590de0ffddaece_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"94\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169145643246\">\n<div data-type=\"problem\" id=\"fs-id1169145643248\">\n<p id=\"fs-id1169145644766\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e80611b064d01ecdbcb8575259d3b241_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#56;&#45;&#52;&#120;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"133\" style=\"vertical-align: -4px;\" \/> find<\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0b961782c20464f4b584b9caa42b24ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-679e9dd9d847ed8e4cd9fb04c8ff0057_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"60\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169145844012\">\n<div data-type=\"problem\" id=\"fs-id1169148229326\">\n<p id=\"fs-id1169148229328\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-1ccee924d000f67b01b5ed82ddbb1b00_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#71;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#53;&#120;&#45;&#49;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"133\" style=\"vertical-align: -4px;\" \/> find<\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f044ff5a23d3030f01e94c59bda68dda_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#71;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-885845a3f108fbd6bab02ae032dfe315_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#71;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"46\" style=\"vertical-align: -4px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1169147863238\">\n<p id=\"fs-id1169147863240\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-12a31481e68c5282ddc4e072954e545c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#71;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;&#92;&#115;&#113;&#114;&#116;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"96\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d122fbb11c08f0ba1417b5abc5e90fcb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#71;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"72\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169147768758\">\n<div data-type=\"problem\" id=\"fs-id1169148208329\">\n<p id=\"fs-id1169148208331\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-fc8bc5550be0b07f3ec2785c5bc47298_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#71;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#52;&#120;&#43;&#49;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"133\" style=\"vertical-align: -4px;\" \/> find<\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-906d68a2f82d8c8d401e4c4604e2f094_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#71;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"48\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-885845a3f108fbd6bab02ae032dfe315_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#71;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"46\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169147719067\">\n<div data-type=\"problem\" id=\"fs-id1169147719070\">\n<p id=\"fs-id1169147700129\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e55d58a282a21d1f8015c718fa2499e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#91;&#51;&#93;&#123;&#50;&#120;&#45;&#52;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"129\" style=\"vertical-align: -4px;\" \/> find<\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-1c932e681a0da3ff9039c0cfbef9f737_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"34\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-82a8451ccbea9dd2f47b6b69e1586f07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"55\" style=\"vertical-align: -4px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1169147977948\">\n<p id=\"fs-id1169147977950\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-003c12226528945543228fd128a2e67c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"66\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-304a262312c775ff771e846cd21eb5f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"94\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169147949679\">\n<div data-type=\"problem\">\n<p id=\"fs-id1169145662640\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-da98fdf8216e5dba56d8d73a4ff72ea2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#91;&#51;&#93;&#123;&#55;&#120;&#45;&#49;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"129\" style=\"vertical-align: -4px;\" \/> find<\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-49fcaf9fe488cacd08d464d30c0c480c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"34\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-05a463dd742637bf2d051da1369c3a23_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"55\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169148229958\">\n<div data-type=\"problem\" id=\"fs-id1169148229960\">\n<p id=\"fs-id1169148229963\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-2bccd351e306a78c1a1f779fc07ee988_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#91;&#51;&#93;&#123;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"129\" style=\"vertical-align: -4px;\" \/> find<\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-290021335f8d9db8fe0ca90975fe52e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"49\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8734931be1d2c4f5b221799be5fb8446_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"43\" style=\"vertical-align: -4px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1169141298382\">\n<p id=\"fs-id1169141298384\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-90a8375d6c1388fc636847d01d20458c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"82\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-dca6284f55924bc063391faf096babd9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;&#92;&#115;&#113;&#114;&#116;&#91;&#51;&#93;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"93\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169148233516\">\n<div data-type=\"problem\" id=\"fs-id1169143534313\">\n<p id=\"fs-id1169143534315\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b91c6526a42fd32b4e9c5d14d7281d7d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#91;&#51;&#93;&#123;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#52;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"129\" style=\"vertical-align: -4px;\" \/> find<\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-290021335f8d9db8fe0ca90975fe52e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"49\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8734931be1d2c4f5b221799be5fb8446_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"43\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169147750980\">\n<div data-type=\"problem\" id=\"fs-id1169147750982\">\n<p id=\"fs-id1169145843952\">For the function<\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-4832be1b42d802a4ef3a4e5ed7ea9142_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#91;&#52;&#93;&#123;&#50;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"108\" style=\"vertical-align: -4px;\" \/> find<\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-3d73c012bc8b5a6f560bea30840502b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"35\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8815bd7781a5bc80d5d01bec8e70c87d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"43\" style=\"vertical-align: -4px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1169140999980\">\n<p id=\"fs-id1169140999982\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b12261fc628a033b58817f7b0f196b8e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"69\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d9c451c3f98dcc76c8d2e0bb8b673dc6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"68\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169145578894\">\n<div data-type=\"problem\" id=\"fs-id1169147878606\">\n<p id=\"fs-id1169147878608\">For the function<\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8de1c60c8da65b2edc304f2af4f4cdfd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#91;&#52;&#93;&#123;&#51;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"108\" style=\"vertical-align: -4px;\" \/> find<\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-3d73c012bc8b5a6f560bea30840502b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"35\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e2d15f1465e8ad2b3d524cbce299db86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"43\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169143303481\">\n<div data-type=\"problem\" id=\"fs-id1169143303483\">\n<p id=\"fs-id1169143303485\">For the function<\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-46437a40ee52e2a21f4880e7ec488a03_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#91;&#52;&#93;&#123;&#52;&#45;&#52;&#120;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"129\" style=\"vertical-align: -4px;\" \/> find<\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0ef2b6c65c15b3dab9cdab30a64cd96f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"34\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-509f3b07987f0f1e75e9db8e5bae79e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"55\" style=\"vertical-align: -4px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1169143520298\">\n<p id=\"fs-id1169145640196\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-1de932db937dbdef508a418ecd01d313_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"67\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d27b627a63246d461d0580b9c5920af2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"80\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169147966879\">\n<div data-type=\"problem\" id=\"fs-id1169143614137\">\n<p id=\"fs-id1169143614139\">For the function<\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-cb548cec0d07285488b73653414f78ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#91;&#52;&#93;&#123;&#56;&#45;&#52;&#120;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"129\" style=\"vertical-align: -4px;\" \/> find<\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-528f14950ec2cc9bb8e68733dd7929d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"48\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-1d648c116745c7ac45af1bac8e06f1bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"42\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<p id=\"fs-id1169142246848\"><strong data-effect=\"bold\">Find the Domain of a Radical Function<\/strong><\/p>\n<p id=\"fs-id1169143520330\">In the following exercises, find the domain of the function and write the domain in interval notation.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1169143520333\">\n<div data-type=\"problem\" id=\"fs-id1169143520335\">\n<p id=\"fs-id1169143520337\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a3136396450556edc87da0eaa8f508e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#51;&#120;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"126\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169141036432\">\n<p id=\"fs-id1169141036434\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f452b85094f87e39944b058d0dad384f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"47\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169148229556\">\n<div data-type=\"problem\" id=\"fs-id1169141030517\">\n<p id=\"fs-id1169141030519\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0aaa44baf9c0d5515f61d6a731db599c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#52;&#120;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"126\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169147816115\">\n<div data-type=\"problem\" id=\"fs-id1169147816117\">\n<p id=\"fs-id1169147816119\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-4707f8dfae246d679f39ac16247da6a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#45;&#51;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"124\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169143492471\">\n<p id=\"fs-id1169148230560\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-aed1eaaf2ad10c1f5a6b10acc7e5c78c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#44;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#93;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"46\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169143576214\">\n<div data-type=\"problem\" id=\"fs-id1169147849778\">\n<p id=\"fs-id1169147849780\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d39e3a51a66eaceeb5ab1da72ef7b42c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#56;&#45;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"115\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169142417344\">\n<div data-type=\"problem\" id=\"fs-id1169142417346\">\n<p id=\"fs-id1169142417348\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b73bed194277d2ae854ac6463c1561e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#120;&#45;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"108\" style=\"vertical-align: -12px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169145747993\">\n<p id=\"fs-id1169145747996\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b3103559f9a65200f03c9dd13b132df4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"47\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169145494672\">\n<div data-type=\"problem\" id=\"fs-id1169145494674\">\n<p id=\"fs-id1169145494676\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-1616bc9156952f8ffcbd1b5657e59071_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#125;&#123;&#120;&#43;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"108\" style=\"vertical-align: -12px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169145621319\">\n<div data-type=\"problem\" id=\"fs-id1169143305828\">\n<p id=\"fs-id1169143305830\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7da377e36710181f7c460ee605bd2822_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#120;&#43;&#51;&#125;&#123;&#120;&#45;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"109\" style=\"vertical-align: -12px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169148125882\">\n<p id=\"fs-id1169148125884\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ab769744d33ea609d3c92fba829c7d95_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#93;&#92;&#99;&#117;&#112;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"126\" style=\"vertical-align: -5px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169147878752\">\n<div data-type=\"problem\" id=\"fs-id1169147878754\">\n<p id=\"fs-id1169141015076\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-bd8704cca243d4c897b81befb0380a75_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#120;&#45;&#49;&#125;&#123;&#120;&#43;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"109\" style=\"vertical-align: -12px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169141298449\">\n<div data-type=\"problem\" id=\"fs-id1169141298451\">\n<p id=\"fs-id1169141298453\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-43bd140c6eca23cfa5065143a0de5f36_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#91;&#51;&#93;&#123;&#56;&#120;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"125\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169147841328\">\n<p id=\"fs-id1169147841330\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-90eaa2f0f55290692476556ec134a082_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169143581471\">\n<div data-type=\"problem\" id=\"fs-id1169143581474\">\n<p id=\"fs-id1169143581476\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a6a7f7696e7111f61a04b45a77b4d916_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#91;&#51;&#93;&#123;&#54;&#120;&#43;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"125\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169141036489\">\n<div data-type=\"problem\" id=\"fs-id1169141036492\">\n<p id=\"fs-id1169141036494\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d828dbe77584e8c29ca29896a20010d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#91;&#51;&#93;&#123;&#52;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"144\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169145494092\">\n<p id=\"fs-id1169145494094\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-90eaa2f0f55290692476556ec134a082_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169143533398\">\n<div data-type=\"problem\" id=\"fs-id1169143533400\">\n<p id=\"fs-id1169145608627\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e8035b6dcb7dc9632c36de0e5c3ac3b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#91;&#51;&#93;&#123;&#54;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"144\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169143614237\">\n<div data-type=\"problem\" id=\"fs-id1169143614239\">\n<p id=\"fs-id1169143614154\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8dc8d0ab35fd90402c8878f2e436a2c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#91;&#52;&#93;&#123;&#56;&#120;&#43;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"130\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169143305858\">\n<p id=\"fs-id1169143305860\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-19f579e7e10cca2712547b3343078943_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#56;&#125;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"61\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169148097678\">\n<div data-type=\"problem\" id=\"fs-id1169148097680\">\n<p id=\"fs-id1169148097682\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-cd0b0589aa2182714489a2e2a9bf4c3e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#91;&#52;&#93;&#123;&#49;&#48;&#45;&#55;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"139\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169145785903\">\n<div data-type=\"problem\" id=\"fs-id1169145785905\">\n<p id=\"fs-id1169145785908\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-db0a3b6d52be65301e75fd10d823ea79_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#71;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#91;&#53;&#93;&#123;&#50;&#120;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"130\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169141015060\">\n<p id=\"fs-id1169141015062\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-90eaa2f0f55290692476556ec134a082_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169147947981\">\n<div data-type=\"problem\" id=\"fs-id1169147947983\">\n<p id=\"fs-id1169147947985\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-aa6ba26b005a45a15f19abe5a1ff05c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#71;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#91;&#53;&#93;&#123;&#54;&#120;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"130\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1169147878727\"><strong data-effect=\"bold\">Graph Radical Functions<\/strong><\/p>\n<p id=\"fs-id1169143681608\">In the following exercises, <span class=\"token\">\u24d0<\/span> find the domain of the function <span class=\"token\">\u24d1<\/span> graph the function <span class=\"token\">\u24d2<\/span> use the graph to determine the range.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1169143681624\">\n<div data-type=\"problem\" id=\"fs-id1169143681627\">\n<p id=\"fs-id1169143681629\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-43c17acca432bef6d69ec5e666e5ac4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#120;&#43;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"117\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169148218613\">\n<p id=\"fs-id1169148218615\"><span class=\"token\">\u24d0<\/span> domain: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-eaca35a24c3f83e7c2b5ab8dad804b6f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#45;&#49;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"57\" style=\"vertical-align: -5px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d1<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span data-type=\"media\" id=\"fs-id1169148132216\" data-alt=\"The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 1 to 7. The y-axis runs from negative 2 to 10. The function has a starting point at (negative 1, 0) and goes through the points (0, 1) and (3, 2).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_08_07_305_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 1 to 7. The y-axis runs from negative 2 to 10. The function has a starting point at (negative 1, 0) and goes through the points (0, 1) and (3, 2).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-2640870d7533edf8778f6e64ee0db9c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#48;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"44\" style=\"vertical-align: -5px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169148117665\">\n<div data-type=\"problem\" id=\"fs-id1169148117667\">\n<p id=\"fs-id1169148117669\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-31dba1e5d91fa44f13506443c9001dc5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#120;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"117\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169145720248\">\n<div data-type=\"problem\" id=\"fs-id1169145720250\">\n<p id=\"fs-id1169145720252\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-093a372d7bccc123f572867cd3cbefc2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#120;&#43;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"115\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169148125839\">\n<p id=\"fs-id1169148125841\"><span class=\"token\">\u24d0<\/span> domain: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-14a619da6584cff593394b1bf3a1b04c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#45;&#52;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"57\" style=\"vertical-align: -5px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d1<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span data-type=\"media\" id=\"fs-id1169143614188\" data-alt=\"The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 2 to 6. The function has a starting point at (negative 4, 0) and goes through the points (negative 3, 1) and (0, 2).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_08_07_307_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 2 to 6. The function has a starting point at (negative 4, 0) and goes through the points (negative 3, 1) and (0, 2).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-2640870d7533edf8778f6e64ee0db9c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#48;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"44\" style=\"vertical-align: -5px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169141047999\">\n<div data-type=\"problem\" id=\"fs-id1169141048001\">\n<p id=\"fs-id1169141048004\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e6ee332b5fe12a4091011349679cb2ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#120;&#45;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"115\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169145925291\">\n<div data-type=\"problem\" id=\"fs-id1169145925293\">\n<p id=\"fs-id1169145925295\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-6bb5bd846b03975ba7ffff6875d2c09b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#120;&#125;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"116\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169145925320\">\n<p id=\"fs-id1169141472915\"><span class=\"token\">\u24d0<\/span> domain: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-2640870d7533edf8778f6e64ee0db9c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#48;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"44\" style=\"vertical-align: -5px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d1<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span data-type=\"media\" id=\"fs-id1169141472943\" data-alt=\"The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from 0 to 8. The y-axis runs from 0 to 8. The function has a starting point at (0, 2) and goes through the points (1, 3) and (4, 4).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_08_07_309_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from 0 to 8. The y-axis runs from 0 to 8. The function has a starting point at (0, 2) and goes through the points (1, 3) and (4, 4).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8eaeb3bff1145b627e5b8f6ec4e7bb43_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#50;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"44\" style=\"vertical-align: -5px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169143637756\">\n<div data-type=\"problem\" id=\"fs-id1169143637759\">\n<p id=\"fs-id1169143637761\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8b9bc24c1eff2670364017fb3edfc1e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#120;&#125;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"116\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169148096679\">\n<div data-type=\"problem\" id=\"fs-id1169148096681\">\n<p id=\"fs-id1169148096683\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f7209f1e1666a26f16b85e4aa6aba34c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;&#92;&#115;&#113;&#114;&#116;&#123;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"94\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169148096706\">\n<p id=\"fs-id1169148096708\"><span class=\"token\">\u24d0<\/span> domain: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-2640870d7533edf8778f6e64ee0db9c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#48;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"44\" style=\"vertical-align: -5px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d1<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span data-type=\"media\" id=\"fs-id1169141373744\" data-alt=\"The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from 0 to 8. The y-axis runs from 0 to 8. The function has a starting point at (0, 0) and goes through the points (1, 2) and (4, 4).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_08_07_311_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from 0 to 8. The y-axis runs from 0 to 8. The function has a starting point at (0, 0) and goes through the points (1, 2) and (4, 4).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-2640870d7533edf8778f6e64ee0db9c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#48;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"44\" style=\"vertical-align: -5px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169141373780\">\n<div data-type=\"problem\" id=\"fs-id1169148049774\">\n<p id=\"fs-id1169148049776\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b5b43e7c94669da33100c14c9ce4fac0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#51;&#92;&#115;&#113;&#114;&#116;&#123;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"94\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169145573813\">\n<div data-type=\"problem\" id=\"fs-id1169145573815\">\n<p id=\"fs-id1169145573817\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d561b1f272d0927a226405f429625699_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#51;&#45;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"117\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169145748017\">\n<p id=\"fs-id1169145748019\"><span class=\"token\">\u24d0<\/span> domain: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-75aa32cd731b55282ba9fea21f217c0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#93;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"44\" style=\"vertical-align: -5px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d1<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span data-type=\"media\" id=\"fs-id1169145748049\" data-alt=\"The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 6 to 4. The y-axis runs from 0 to 8. The function has a starting point at (3, 0) and goes through the points (2, 1), (negative 1, 2), and (negative 6, 3).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_08_07_313_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 6 to 4. The y-axis runs from 0 to 8. The function has a starting point at (3, 0) and goes through the points (2, 1), (negative 1, 2), and (negative 6, 3).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-2640870d7533edf8778f6e64ee0db9c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#48;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"44\" style=\"vertical-align: -5px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169143305900\">\n<div data-type=\"problem\" id=\"fs-id1169143305902\">\n<p id=\"fs-id1169143305905\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ca6099178ff3c731b7bcb41784b89359_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#52;&#45;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"117\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169143519080\">\n<div data-type=\"problem\" id=\"fs-id1169143519082\">\n<p id=\"fs-id1169143519085\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c8e6d1b2223217394e8781f012d0cd96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#115;&#113;&#114;&#116;&#123;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"85\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169143519108\">\n<p id=\"fs-id1169143519110\"><span class=\"token\">\u24d0<\/span> domain: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-2640870d7533edf8778f6e64ee0db9c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#48;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"44\" style=\"vertical-align: -5px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d1<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span data-type=\"media\" id=\"fs-id1169147797041\" data-alt=\"The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from 0 to 8. The y-axis runs from negative 8 to 0. The function has a starting point at (0, 0) and goes through the points (1, negative 1) and (4, negative 2).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_08_07_315_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from 0 to 8. The y-axis runs from negative 8 to 0. The function has a starting point at (0, 0) and goes through the points (1, negative 1) and (4, negative 2).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e17506f6a3d2c4bacadf719b026fd442_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#93;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"44\" style=\"vertical-align: -5px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169147797078\">\n<div data-type=\"problem\" id=\"fs-id1169147797080\">\n<p id=\"fs-id1169147797082\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-472df35733842c6a1a04facece02584a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#115;&#113;&#114;&#116;&#123;&#120;&#125;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"114\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169145977421\">\n<div data-type=\"problem\" id=\"fs-id1169145977423\">\n<p id=\"fs-id1169145977426\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ff0fc0458e39b823ebdca5f4b113c9cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#91;&#51;&#93;&#123;&#120;&#43;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"118\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169145977454\">\n<p id=\"fs-id1169145977456\"><span class=\"token\">\u24d0<\/span> domain: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-90eaa2f0f55290692476556ec134a082_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d1<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span data-type=\"media\" id=\"fs-id1169145977630\" data-alt=\"The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The function has a center point at (negative 1, 0) and goes through the points (negative 2, negative 1) and (0, 1).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_08_07_317_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The function has a center point at (negative 1, 0) and goes through the points (negative 2, negative 1) and (0, 1).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-90eaa2f0f55290692476556ec134a082_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169145977667\">\n<div data-type=\"problem\" id=\"fs-id1169145977670\">\n<p id=\"fs-id1169145977672\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ad383e42eaafe233a64a67f906f809a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#91;&#51;&#93;&#123;&#120;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"118\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169148062987\">\n<div data-type=\"problem\" id=\"fs-id1169148062989\">\n<p id=\"fs-id1169148062991\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ca40c26b9bd8828346eec669fa93f743_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#91;&#51;&#93;&#123;&#120;&#43;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"116\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169148063020\">\n<p id=\"fs-id1169148063022\"><span class=\"token\">\u24d0<\/span> domain: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-90eaa2f0f55290692476556ec134a082_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d1<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span data-type=\"media\" id=\"fs-id1169147720433\" data-alt=\"The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The function has a center point at (negative 4, 0) and goes through the points (negative 3, negative 1) and (negative 1, 1).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_08_07_319_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The function has a center point at (negative 4, 0) and goes through the points (negative 3, negative 1) and (negative 1, 1).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-90eaa2f0f55290692476556ec134a082_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169147720471\">\n<div data-type=\"problem\" id=\"fs-id1169147720473\">\n<p id=\"fs-id1169147720475\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-383e1981a91ccc93fb47fe4b90d120a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#91;&#51;&#93;&#123;&#120;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"116\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169143316905\">\n<div data-type=\"problem\" id=\"fs-id1169143316907\">\n<p id=\"fs-id1169143316909\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-576abc85a87a50d8cea6c44df2b08954_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#91;&#51;&#93;&#123;&#120;&#125;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"118\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169143316937\">\n<p id=\"fs-id1169143316939\"><span class=\"token\">\u24d0<\/span> domain: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-90eaa2f0f55290692476556ec134a082_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d1<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span data-type=\"media\" id=\"fs-id1169143316969\" data-alt=\"The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 2 to 6. The function has a center point at (0, 3) and goes through the points (negative 1, 2) and (1, 4).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_08_07_321_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 2 to 6. The function has a center point at (0, 3) and goes through the points (negative 1, 2) and (1, 4).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-90eaa2f0f55290692476556ec134a082_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169141376312\">\n<div data-type=\"problem\" id=\"fs-id1169141376314\">\n<p id=\"fs-id1169141376316\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f31507b945ae7e6ce98fd1a5e9f12adb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#91;&#51;&#93;&#123;&#120;&#125;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"118\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169145579077\">\n<div data-type=\"problem\" id=\"fs-id1169145579079\">\n<p id=\"fs-id1169145579081\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f70d73e8f09a85aae487c4509e959876_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#91;&#51;&#93;&#123;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"86\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169145579105\">\n<p id=\"fs-id1169145579107\"><span class=\"token\">\u24d0<\/span> domain: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-90eaa2f0f55290692476556ec134a082_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d1<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span data-type=\"media\" id=\"fs-id1169145579137\" data-alt=\"The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The function has a center point at (0, 0) and goes through the points (1, 1) and (negative 1, negative 1).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_08_07_323_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The function has a center point at (0, 0) and goes through the points (1, 1) and (negative 1, negative 1).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-90eaa2f0f55290692476556ec134a082_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169147987528\">\n<div data-type=\"problem\" id=\"fs-id1169147987530\">\n<p id=\"fs-id1169147987532\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-99d19344c698bcca77f3c1cff76fcc08_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#115;&#113;&#114;&#116;&#91;&#51;&#93;&#123;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"86\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169148063131\">\n<div data-type=\"problem\" id=\"fs-id1169148063133\">\n<p id=\"fs-id1169148063135\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ddf9e870ab7d67cb24c7c87cfe4fb602_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;&#92;&#115;&#113;&#114;&#116;&#91;&#51;&#93;&#123;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"97\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169148063160\">\n<p id=\"fs-id1169148063163\"><span class=\"token\">\u24d0<\/span> domain: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-90eaa2f0f55290692476556ec134a082_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d1<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span data-type=\"media\" id=\"fs-id1169148063192\" data-alt=\"The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The function has a center point at (0, 0) and goes through the points (1, 2) and (negative 1, negative 2).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_08_07_325_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The function has a center point at (0, 0) and goes through the points (1, 2) and (negative 1, negative 2).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-90eaa2f0f55290692476556ec134a082_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169147725430\">\n<div data-type=\"problem\" id=\"fs-id1169147725432\">\n<p id=\"fs-id1169147725434\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-680e1cd217a6c6c6909aeb229cfe873b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#50;&#92;&#115;&#113;&#114;&#116;&#91;&#51;&#93;&#123;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"111\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"writing\" data-depth=\"2\" id=\"fs-id1169148053100\">\n<h4 data-type=\"title\">Writing Exercises<\/h4>\n<div data-type=\"exercise\" id=\"fs-id1169148053107\">\n<div data-type=\"problem\" id=\"fs-id1169148053109\">\n<p id=\"fs-id1169148053111\">Explain how to find the domain of a fourth root function.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169148053115\">\n<p id=\"fs-id1169148053117\">Answers will vary.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169148053123\">\n<div data-type=\"problem\" id=\"fs-id1169148053125\">\n<p id=\"fs-id1169148053127\">Explain how to find the domain of a fifth root function.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169148053139\">\n<div data-type=\"problem\" id=\"fs-id1169148053141\">\n<p id=\"fs-id1169148053143\">Explain why <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0780d3d7bf156a61f7a6a9f68d608b29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#115;&#113;&#114;&#116;&#91;&#51;&#93;&#123;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"60\" style=\"vertical-align: -4px;\" \/> is a function.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1169148053161\">\n<p id=\"fs-id1169148053163\">Answers will vary.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1169148053168\">\n<div data-type=\"problem\" id=\"fs-id1169148053171\">\n<p id=\"fs-id1169148053173\">Explain why the process of finding the domain of a radical function with an even index is different from the process when the index is odd.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"2\" id=\"fs-id1169148053187\">\n<h4 data-type=\"title\">Self Check<\/h4>\n<p id=\"fs-id1169148053192\"><span class=\"token\">\u24d0<\/span> After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.<\/p>\n<p><span data-type=\"media\" id=\"fs-id1169143519206\" data-alt=\"The table has 4 columns and 4 rows. The first row is a header row with the headers \u201cI can\u2026\u201d, \u201cConfidently\u201d, \u201cWith some help.\u201d, and \u201cNo \u2013 I don\u2019t get it!\u201d. The first column contains the phrases \u201cevaluate a radical function\u201d, \u201cfind the domain of a radical function\u201d, and \u201cgraph a radical function\u201d. The other columns are left blank so the learner can indicate their level of understanding.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_08_07_201_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The table has 4 columns and 4 rows. The first row is a header row with the headers \u201cI can\u2026\u201d, \u201cConfidently\u201d, \u201cWith some help.\u201d, and \u201cNo \u2013 I don\u2019t get it!\u201d. The first column contains the phrases \u201cevaluate a radical function\u201d, \u201cfind the domain of a radical function\u201d, and \u201cgraph a radical function\u201d. The other columns are left blank so the learner can indicate their level of understanding.\" \/><\/span><\/p>\n<p id=\"fs-id1169148053206\"><span class=\"token\">\u24d1<\/span> What does this checklist tell you about your mastery of this section? What steps will you take to improve?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"glossary\" class=\"textbox shaded\">\n<h3 data-type=\"glossary-title\">Glossary<\/h3>\n<dl id=\"fs-id1169143519223\">\n<dt>radical function<\/dt>\n<dd id=\"fs-id1169143519229\">A radical function is a function that is defined by a radical expression.<\/dd>\n<\/dl>\n<\/div>\n","protected":false},"author":103,"menu_order":8,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-3653","chapter","type-chapter","status-publish","hentry"],"part":3472,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/pressbooks\/v2\/chapters\/3653","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/wp\/v2\/users\/103"}],"version-history":[{"count":0,"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/pressbooks\/v2\/chapters\/3653\/revisions"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/pressbooks\/v2\/parts\/3472"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/pressbooks\/v2\/chapters\/3653\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/wp\/v2\/media?parent=3653"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/pressbooks\/v2\/chapter-type?post=3653"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/wp\/v2\/contributor?post=3653"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/wp\/v2\/license?post=3653"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}