{"id":1809,"date":"2019-08-13T18:24:38","date_gmt":"2019-08-13T22:24:38","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=back-matter&p=1809"},"modified":"2019-08-13T19:18:08","modified_gmt":"2019-08-13T23:18:08","slug":"answer-key-11-1","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/back-matter\/answer-key-11-1\/","title":{"raw":"Answer Key 11.1","rendered":"Answer Key 11.1"},"content":{"raw":"[latexpage]\r\n
    \r\n \t
  1. \r\n
      \r\n \t
    1. No<\/li>\r\n \t
    2. Yes<\/li>\r\n \t
    3. No<\/li>\r\n \t
    4. Yes<\/li>\r\n \t
    5. Yes<\/li>\r\n \t
    6. No<\/li>\r\n \t
    7. Yes<\/li>\r\n \t
    8. \\(y^2=1+x^2\\)\r\n\\(y=\\pm \\sqrt{1+x^2}\\)\r\nNo<\/li>\r\n \t
    9. \\(\\sqrt{y}=2-x\\)\r\n\\(y=(2-x)^2\\)\r\nYes<\/li>\r\n \t
    10. \\(y^2=1-x^2\\)\r\n\\(y=\\pm \\sqrt{1-x^2}\\)\r\nNo<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t
    11. All real numbers \\(-\\infty, \\infty\\)<\/li>\r\n \t
    12. \\(\\begin{array}{rrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n5&-&4x&\\ge &0 \\\\\r\n-5&&&&-5 \\\\\r\n\\midrule\r\n&&\\dfrac{-4x}{-4}&\\ge &\\dfrac{-5}{-4} \\\\ \\\\\r\n&&x&\\le &\\dfrac{5}{4} \\\\\r\n\\end{array}\\)\r\n\r\n\\(\\left(-\\infty, \\dfrac{5}{4}\\right]\\)<\/li>\r\n \t
    13. \\(t^2\\neq 0\\)\r\n\\(t\\neq \\sqrt{0}\\text{ or }0\\)<\/li>\r\n \t
    14. All real or \\((-\\infty, \\infty)\\)<\/li>\r\n \t
    15. \\(\\begin{array}{rrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\nt^2&+&1&\\neq &0 \\\\\r\n&-&1&&-1 \\\\\r\n\\midrule\r\n&&t^2&\\neq &-1 \\\\\r\n&&t&\\neq & i \\\\ \\\\\r\n&&t&=&\\mathbb{R}\r\n\\end{array}\\)<\/li>\r\n \t
    16. \\(\\begin{array}{rrrrr}\r\n\\\\ \\\\\r\nx&-&16&\\ge &0 \\\\\r\n&+&16&&+16 \\\\\r\n\\midrule\r\n&&x&\\ge &16 \\\\\r\n\\end{array}\\)\r\n\r\n\\([16, \\infty)\\)<\/li>\r\n \t
    17. \\(x^2-3x-4\\neq 0\\)\r\n\\((x-4)(x+1)\\neq 0\\)\r\n\\(x\\neq 4,1\\)<\/li>\r\n \t
    18. \\(\\begin{array}{ll}\r\n\\\\ \\\\ \\\\\r\n\\begin{array}{rrrrr}\r\n\\\\ \\\\\r\n3x&-&12&\\ge &0 \\\\\r\n&+&12&&+12 \\\\\r\n\\midrule\r\n&&\\dfrac{3x}{3}&\\ge &\\dfrac{12}{3} \\\\ \\\\\r\n&&x&\\ge &4\r\n\\end{array}\r\n&\\hspace{0.25in}\r\n\\begin{array}{rrl}\r\n\\\\\r\nx^2-25&\\neq &0 \\\\\r\n(x-5)(x+5)&\\neq &0 \\\\\r\nx&\\neq &5, -5 \\\\ \\\\\r\n\\therefore x&\\ge &4, \\neq \\pm 5\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
    19. \\(\\begin{array}{rrl}\r\n\\\\\r\ng(0)&=&\\cancel{4(0)}-4 \\\\\r\n&=&-4\r\n\\end{array}\\)<\/li>\r\n \t
    20. \\(\\begin{array}{rrl}\r\n\\\\\r\ng(2)&=&-3\\cdot 5^{-2} \\\\\r\n&=&-\\dfrac{3}{25}\r\n\\end{array}\\)<\/li>\r\n \t
    21. \\(\\begin{array}{rrl}\r\n\\\\\r\nf(-9)&=&(-9)^2+4 \\\\\r\n&=&81+4 \\\\\r\n&=&85\r\n\\end{array}\\)<\/li>\r\n \t
    22. \\(\\begin{array}{rrl}\r\n\\\\\r\nf(10)&=&10-3 \\\\\r\n&=&7\r\n\\end{array}\\)<\/li>\r\n \t
    23. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\nf(-2)&=&3^{-2}-2 \\\\ \\\\\r\n&=&\\dfrac{1}{9}-2 \\\\ \\\\\r\n&=&\\dfrac{1}{9}-\\dfrac{18}{9} \\\\ \\\\\r\n&=&-\\dfrac{17}{9}\r\n\\end{array}\\)<\/li>\r\n \t
    24. \\(\\begin{array}{rrl}\r\n\\\\ \\\\\r\nf(2)&=&-3^{2-1}-3 \\\\\r\n&=&-3^1-3 \\\\\r\n&=&-6\r\n\\end{array}\\)<\/li>\r\n \t
    25. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\\r\nk(2)&=&-2\\cdot 4^{2(2)-2} \\\\\r\n&=&-2\\cdot 4^{4-2} \\\\\r\n&=&-2\\cdot 4^2 \\\\\r\n&=&-32\r\n\\end{array}\\)<\/li>\r\n \t
    26. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\np(-2)&=&-2\\cdot 4^{2(-2)+1}+1 \\\\\r\n&=&-2\\cdot 4^{-4+1}+1 \\\\\r\n&=&-2\\cdot 4^{-3}+1 \\\\\r\n&=&-\\dfrac{2}{64}+1 \\\\ \\\\\r\n&=&-\\dfrac{1}{32}+1 \\Rightarrow \\dfrac{-31}{32}\r\n\\end{array}\\)<\/li>\r\n \t
    27. \\(\\begin{array}{rrl}\r\n\\\\\r\nh(-4x)&=&(-4x)^3+2 \\\\\r\n&=&-64x^3+2\r\n\\end{array}\\)<\/li>\r\n \t
    28. \\(\\begin{array}{rrl}\r\n\\\\ \\\\\r\nh(n+2)&=&4(n+2)+2 \\\\\r\n&=&4n+8+2 \\\\\r\n&=&4n+10\r\n\\end{array}\\)<\/li>\r\n \t
    29. \\(\\begin{array}{rrl}\r\n\\\\ \\\\\r\nh(-1+x)&=&3(-1+x)+2 \\\\\r\n&=&-3+3x+2 \\\\\r\n&=&3x-1\r\n\\end{array}\\)<\/li>\r\n \t
    30. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\\r\nh\\left(\\dfrac{1}{3}\\right)&=&-3\\cdot 2^{\\frac{1}{3}+3} \\\\\r\n&=& -2^3\\cdot 3\\sqrt[3]{2}\\\\\r\n&=&-8\\cdot 3\\sqrt[3]{2} \\\\\r\n&=&-24 \\sqrt[3]{2}\r\n\\end{array}\\)<\/li>\r\n \t
    31. \\(\\begin{array}{rrl}\r\n\\\\\r\nh(x^4)&=&(x^4)^2+1 \\\\\r\n&=&x^8+1\r\n\\end{array}\\)<\/li>\r\n \t
    32. \\(\\begin{array}{rrl}\r\n\\\\\r\nh(t^2)&=&(t^2)^2+t \\\\\r\n&=&t^4+t\r\n\\end{array}\\)<\/li>\r\n \t
    33. \\(\\begin{array}{rrl}\r\n\\\\\r\nf(0)&=&|\\cancel{3(0)}+1|+1 \\\\\r\n&=&1+1\\text{ or }2\r\n\\end{array}\\)<\/li>\r\n \t
    34. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\\r\nf(-6)&=&-2 |-(-6)-2 | +1 \\\\\r\n&=&-2 |6-2| + 1 \\\\\r\n&=& -2(4)+1 \\\\\r\n&=& -8 + 1\\text{ or }-7\r\n\\end{array}\\)<\/li>\r\n \t
    35. \\(\\begin{array}{rrl}\r\n\\\\\r\nf(10)&=&|10+3| \\\\\r\n&=&13\r\n\\end{array}\\)<\/li>\r\n \t
    36. \\(\\begin{array}{rrl}\r\n\\\\ \\\\\r\np(5)&=&-|5|+1 \\\\\r\n&=&-5+1 \\\\\r\n&=& -4\r\n\\end{array}\\)<\/li>\r\n<\/ol>","rendered":"
        \n
      1. \n
          \n
        1. No<\/li>\n
        2. Yes<\/li>\n
        3. No<\/li>\n
        4. Yes<\/li>\n
        5. Yes<\/li>\n
        6. No<\/li>\n
        7. Yes<\/li>\n
        8. \"y^2=1+x^2\"
          \n\"y=\pm \sqrt{1+x^2}\"
          \nNo<\/li>\n
        9. \"\sqrt{y}=2-x\"
          \n\"y=(2-x)^2\"
          \nYes<\/li>\n
        10. \"y^2=1-x^2\"
          \n\"y=\pm \sqrt{1-x^2}\"
          \nNo<\/li>\n<\/ol>\n<\/li>\n
        11. All real numbers \"-\infty, \infty\"<\/li>\n
        12. \"\begin{array}{rrrrr}\n

          \"\left(-\infty, \dfrac{5}{4}\right]\"<\/li>\n

        13. \"t^2\neq 0\"
          \n\"t\neq \sqrt{0}\text{ or }0\"<\/li>\n
        14. All real or \"(-\infty, \infty)\"<\/li>\n
        15. \"\begin{array}{rrrrr}<\/li>\n
        16. \"\begin{array}{rrrrr}\n

          \"[16, \infty)\"<\/li>\n

        17. \"x^2-3x-4\neq 0\"
          \n\"(x-4)(x+1)\neq 0\"
          \n\"x\neq 4,1\"<\/li>\n
        18. \"\begin{array}{ll}<\/li>\n
        19. \"\begin{array}{rrl}<\/li>\n
        20. \"\begin{array}{rrl}<\/li>\n
        21. \"\begin{array}{rrl}<\/li>\n
        22. \"\begin{array}{rrl}<\/li>\n
        23. \"\begin{array}{rrl}<\/li>\n
        24. \"\begin{array}{rrl}<\/li>\n
        25. \"\begin{array}{rrl}<\/li>\n
        26. \"\begin{array}{rrl}<\/li>\n
        27. \"\begin{array}{rrl}<\/li>\n
        28. \"\begin{array}{rrl}<\/li>\n
        29. \"\begin{array}{rrl}<\/li>\n
        30. \"\begin{array}{rrl}<\/li>\n
        31. \"\begin{array}{rrl}<\/li>\n
        32. \"\begin{array}{rrl}<\/li>\n
        33. \"\begin{array}{rrl}<\/li>\n
        34. \"\begin{array}{rrl}<\/li>\n
        35. \"\begin{array}{rrl}<\/li>\n
        36. \"\begin{array}{rrl}<\/li>\n<\/ol>\n","protected":false},"author":727,"menu_order":102,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"back-matter-type":[],"contributor":[],"license":[],"class_list":["post-1809","back-matter","type-back-matter","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1809","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/users\/727"}],"version-history":[{"count":3,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1809\/revisions"}],"predecessor-version":[{"id":1812,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1809\/revisions\/1812"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1809\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/media?parent=1809"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter-type?post=1809"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/contributor?post=1809"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/license?post=1809"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}