{"id":3058,"date":"2021-06-24T16:26:24","date_gmt":"2021-06-24T20:26:24","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/?post_type=chapter&#038;p=3058"},"modified":"2021-07-12T13:45:26","modified_gmt":"2021-07-12T17:45:26","slug":"2-1-example-of-a-function","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/chapter\/2-1-example-of-a-function\/","title":{"raw":"2.1 Example of a Function","rendered":"2.1 Example of a Function"},"content":{"raw":"<h2>Example 2.1.1<\/h2>\r\nA shirt manufacturer may decide to produce a certain number of shirts of a particular size and style. The first task is to find out the amount of material needed.\r\n\r\nThen,\r\n\r\n[latex]\\begin{align*}\r\n\r\n&amp;\\text{Amount of Material} &amp;= m &amp;\u2192 \\text{DEPENDENT VARIABLE }(y)\\\\\r\n\r\n&amp;\\text{depends on} &amp;&amp;\u2192 \\text{IS A FUNCTION OF}\\\\\r\n\r\n&amp;\\text{Number of Shirts} &amp;= n &amp;\u2192\\text{INDEPENDENT VARIABLE }(x)\r\n\r\n\\end{align*}[\/latex]\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\nA function must be described in such a way that you can find the value of the dependent variable from the value of the independent variable. Three standard ways of doing this are used in this course.\r\n\r\nThey are,\r\n<ul>\r\n \t<li>an equation, which allows you to calculate the value of the dependent variable for each value of the independent variable.<\/li>\r\n \t<li>a table, which lists the value of the dependent variable for each value of the independent variable.<\/li>\r\n \t<li>a graph, which displays the value of the dependent variable for each value of the independent variable.<\/li>\r\n<\/ul>\r\n<h2>Example 2.1.2<\/h2>\r\n<div class=\"textbox__content\">Suppose a series of items are to be marked up by 40% of cost. The selling price (the value wanted) can be described in terms of the cost (the value known) in the following ways:<\/div>\r\n<div><\/div>\r\n<div><img class=\"wp-image-175 size-medium aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-content\/uploads\/sites\/971\/2020\/04\/chap2-costgraph-300x167.png\" alt=\"Graph of the equation S = 1.4C\" width=\"300\" height=\"167\" \/><\/div>\r\n<div><\/div>\r\n&nbsp;\r\n\r\nAll of these approaches give the selling price, \u00a0(dependent variable), as a function of the cost, (independent variable). A function like this, where one variable is a multiple of another, is called <em>direct variation.<\/em>\r\n\r\nNote that such functions follow the algebra convention which states that when single letters are used to stand for variables, multiplication is to be used when no other operation is given, so that\r\n<p style=\"text-align: center\">[latex]1.4 C \\text{ means }1.4\\times C[\/latex]<\/p>\r\n\r\n<div>\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Key Takeaways<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\"><em>Equations provide short descriptions of functions and enable you to find precise values of the dependent variable.<\/em><\/div>\r\n<\/div>\r\n&nbsp;\r\n\r\n<\/div>\r\nAlso, you will follow the graphing convention which requires that the independent variable be drawn on the horizontal axis and equal the dependent variable on the vertical axis.\r\n\r\nEach way of describing functions has its own advantages. Equations have the advantage of providing short descriptions of functions and enabling you to find precise values of the dependent variable when you need them. However, it may be difficult to do the calculation, or to understand the overall behavior of the function.\r\n<div>\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Key Takeaways<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\"><em>Tables give values immediately, without calculation <\/em>...\u00a0 <em>Graphs communicate an overall understanding of the way a function behaves.<\/em><\/div>\r\n<\/div>\r\n&nbsp;\r\n<h2>Your Own Notes<\/h2>\r\n<ul>\r\n \t<li>Are there any notes you want to take from this section? Is there anything you'd like to copy and paste below?<\/li>\r\n \t<li>These notes are for you only (they will not be stored anywhere)<\/li>\r\n \t<li>Make sure to download them at the end to use as a reference<\/li>\r\n<\/ul>\r\n[h5p id=\"1\"]\r\n\r\n<\/div>","rendered":"<h2>Example 2.1.1<\/h2>\n<p>A shirt manufacturer may decide to produce a certain number of shirts of a particular size and style. The first task is to find out the amount of material needed.<\/p>\n<p>Then,<\/p>\n<p>[latex]\\begin{align*}    &\\text{Amount of Material} &= m &\u2192 \\text{DEPENDENT VARIABLE }(y)\\\\    &\\text{depends on} &&\u2192 \\text{IS A FUNCTION OF}\\\\    &\\text{Number of Shirts} &= n &\u2192\\text{INDEPENDENT VARIABLE }(x)    \\end{align*}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>A function must be described in such a way that you can find the value of the dependent variable from the value of the independent variable. Three standard ways of doing this are used in this course.<\/p>\n<p>They are,<\/p>\n<ul>\n<li>an equation, which allows you to calculate the value of the dependent variable for each value of the independent variable.<\/li>\n<li>a table, which lists the value of the dependent variable for each value of the independent variable.<\/li>\n<li>a graph, which displays the value of the dependent variable for each value of the independent variable.<\/li>\n<\/ul>\n<h2>Example 2.1.2<\/h2>\n<div class=\"textbox__content\">Suppose a series of items are to be marked up by 40% of cost. The selling price (the value wanted) can be described in terms of the cost (the value known) in the following ways:<\/div>\n<div><\/div>\n<div><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-175 size-medium aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-content\/uploads\/sites\/971\/2020\/04\/chap2-costgraph-300x167.png\" alt=\"Graph of the equation S = 1.4C\" width=\"300\" height=\"167\" srcset=\"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-content\/uploads\/sites\/971\/2020\/04\/chap2-costgraph-300x167.png 300w, https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-content\/uploads\/sites\/971\/2020\/04\/chap2-costgraph-65x36.png 65w, https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-content\/uploads\/sites\/971\/2020\/04\/chap2-costgraph-225x125.png 225w, https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-content\/uploads\/sites\/971\/2020\/04\/chap2-costgraph-350x195.png 350w, https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-content\/uploads\/sites\/971\/2020\/04\/chap2-costgraph.png 583w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/div>\n<div><\/div>\n<p>&nbsp;<\/p>\n<p>All of these approaches give the selling price, \u00a0(dependent variable), as a function of the cost, (independent variable). A function like this, where one variable is a multiple of another, is called <em>direct variation.<\/em><\/p>\n<p>Note that such functions follow the algebra convention which states that when single letters are used to stand for variables, multiplication is to be used when no other operation is given, so that<\/p>\n<p style=\"text-align: center\">[latex]1.4 C \\text{ means }1.4\\times C[\/latex]<\/p>\n<div>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Key Takeaways<\/p>\n<\/header>\n<div class=\"textbox__content\"><em>Equations provide short descriptions of functions and enable you to find precise values of the dependent variable.<\/em><\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<p>Also, you will follow the graphing convention which requires that the independent variable be drawn on the horizontal axis and equal the dependent variable on the vertical axis.<\/p>\n<p>Each way of describing functions has its own advantages. Equations have the advantage of providing short descriptions of functions and enabling you to find precise values of the dependent variable when you need them. However, it may be difficult to do the calculation, or to understand the overall behavior of the function.<\/p>\n<div>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Key Takeaways<\/p>\n<\/header>\n<div class=\"textbox__content\"><em>Tables give values immediately, without calculation <\/em>&#8230;\u00a0 <em>Graphs communicate an overall understanding of the way a function behaves.<\/em><\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<h2>Your Own Notes<\/h2>\n<ul>\n<li>Are there any notes you want to take from this section? Is there anything you&#8217;d like to copy and paste below?<\/li>\n<li>These notes are for you only (they will not be stored anywhere)<\/li>\n<li>Make sure to download them at the end to use as a reference<\/li>\n<\/ul>\n<div id=\"h5p-1\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-1\" class=\"h5p-iframe\" data-content-id=\"1\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"Key takeaways, notes and comments from this section document tool.\"><\/iframe><\/div>\n<\/div>\n<\/div>\n","protected":false},"author":883,"menu_order":1,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-3058","chapter","type-chapter","status-publish","hentry"],"part":40,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/chapters\/3058","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/wp\/v2\/users\/883"}],"version-history":[{"count":4,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/chapters\/3058\/revisions"}],"predecessor-version":[{"id":3858,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/chapters\/3058\/revisions\/3858"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/parts\/40"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/chapters\/3058\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/wp\/v2\/media?parent=3058"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/chapter-type?post=3058"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/wp\/v2\/contributor?post=3058"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/wp\/v2\/license?post=3058"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}