{"id":163,"date":"2023-06-21T13:22:39","date_gmt":"2023-06-21T13:22:39","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/graph-linear-functions-2\/"},"modified":"2023-07-03T19:57:51","modified_gmt":"2023-07-03T19:57:51","slug":"graph-linear-functions-2","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/graph-linear-functions-2\/","title":{"raw":"R3.1   The Graph of a Linear Function","rendered":"R3.1   The Graph of a Linear Function"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\">\r\n<h3>Learning Outcome<\/h3>\r\n<ul>\r\n \t<li>Graph linear functions using tables<\/li>\r\n<\/ul>\r\n<\/div>\r\nA helpful first step in graphing a function is to make a table of values. This is particularly useful when you do not know the general shape the function will have. You probably already know that a linear function will be a straight line, but let us make a table first to see how it can be helpful.\r\n\r\nWhen making a table, it is a good idea to include negative values, positive values, and zero to ensure that you do have a linear function.\r\n\r\nMake a table of values for [latex]f(x)=3x+2[\/latex].\r\n\r\nMake a two-column table. Label the columns <i>x<\/i> and <i>f<\/i>(<i>x<\/i>).\r\n<table style=\"width: 20%;\">\r\n<thead>\r\n<tr>\r\n<th style=\"text-align: center;\"><i>x<\/i><\/th>\r\n<th style=\"text-align: center;\"><i>f<\/i>(<i>x<\/i>)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td style=\"text-align: center;\"><\/td>\r\n<td style=\"text-align: center;\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><\/td>\r\n<td style=\"text-align: center;\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nChoose several values for <i>x<\/i> and put them as separate rows in the <i>x<\/i> column. These are YOUR CHOICE - there is no \"right\" or \"wrong\" values to pick, just go for it.\r\n\r\n<i>Tip:<\/i> It is always good to include 0, positive values, and negative values, if possible.\r\n<table style=\"width: 20%; height: 72px;\">\r\n<thead>\r\n<tr style=\"height: 12px;\">\r\n<th style=\"text-align: center; height: 12px;\"><i>x<\/i><\/th>\r\n<th style=\"text-align: center; height: 12px;\"><i>f<\/i>(<i>x<\/i>)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"text-align: center; height: 12px;\">[latex]\u22122[\/latex]<\/td>\r\n<td style=\"text-align: center; height: 12px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"text-align: center; height: 12px;\">[latex]\u22121[\/latex]<\/td>\r\n<td style=\"text-align: center; height: 12px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"text-align: center; height: 12px;\">[latex]0[\/latex]<\/td>\r\n<td style=\"text-align: center; height: 12px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"text-align: center; height: 12px;\">[latex]1[\/latex]<\/td>\r\n<td style=\"text-align: center; height: 12px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"text-align: center; height: 12px;\">[latex]3[\/latex]<\/td>\r\n<td style=\"text-align: center; height: 12px;\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nEvaluate the function for each value of <i>x<\/i>, and write the result in the <i>f<\/i>(<i>x<\/i>) column next to the <i>x<\/i> value you used.\r\n\r\nWhen [latex]x=0[\/latex], [latex]f(0)=3(0)+2=2[\/latex],\r\n\r\n[latex]f(1)=3(1)+2=5[\/latex],\r\n\r\n[latex]f(\u22121)=3(\u22121)+2=\u22123+2=\u22121[\/latex],\u00a0and so on.\r\n<table style=\"width: 20%;\">\r\n<tbody>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong><i>x<\/i><\/strong><\/td>\r\n<td style=\"text-align: center;\"><strong><i>f<\/i>(<i>x<\/i>)<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\">[latex]\u22122[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]\u22124[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\">[latex]\u22121[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]\u22121[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\">[latex]0[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]2[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\">[latex]1[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]5[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\">[latex]3[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]11[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n(Note that your table of values may be different from someone else\u2019s. You may each choose different numbers for <i>x<\/i>.)\r\n\r\nNow that you have a table of values, you can use them to help you draw both the shape and location of the function. <i>Important:<\/i> The graph of the function will show all possible values of <i>x<\/i> and the corresponding values of <i>y<\/i>. This is why the graph is a line and not just the dots that make up the points in our table.\r\n\r\nNow graph [latex]f(x)=3x+2[\/latex].\r\nUsing the table of values we created above, you can think of <i>f<\/i>(<i>x<\/i>) as <i>y. <\/i>Each row forms an ordered pair that you can plot on a coordinate grid.\r\n<table style=\"width: 20%;\">\r\n<tbody>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong><i>x<\/i><\/strong><\/td>\r\n<td style=\"text-align: center;\"><strong><i>f<\/i>(<i>x<\/i>)<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\">[latex]\u22122[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]\u22124[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\">[latex]\u22121[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]\u22121[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\">[latex]0[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]2[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\">[latex]1[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]5[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\">[latex]3[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]11[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nPlot the points.\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/121\/2016\/04\/18232424\/image005.gif\" alt=\"The points negative 2, negative 4; the point negative 1, negative 1; the point 0, 2; the point 1, 5; the point 3, 11.\" width=\"322\" height=\"353\" \/>\r\n\r\nSince the points lie on a line, use a straight edge to draw the line. Try to go through each point without moving the straight edge.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/121\/2016\/04\/18232426\/image006.gif\" alt=\"A line through the points in the previous graph.\" width=\"322\" height=\"353\" \/>\r\n\r\n&nbsp;\r\n\r\nLet us try another one. Before you look at the answer, try to make the table yourself and draw the graph on a piece of paper.\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nGraph [latex]f(x)=\u2212x+1[\/latex].\r\n\r\n[reveal-answer q=\"748367\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"748367\"]\r\n\r\nStart with a table of values. You can choose different values for <i>x<\/i>, but once again, it is helpful to include [latex]0[\/latex], some positive values, and some negative values.\r\n\r\nIf you think of <i>f<\/i>(<i>x<\/i>) as <i>y,<\/i> each row forms an ordered pair that you can plot on a coordinate grid.\r\n<p style=\"text-align: center;\">[latex]f(\u22122)=\u2212(\u22122)+1=2+1=3\\\\f(\u22121)=\u2212(\u22121)+1=1+1=2\\\\f(0)=\u2212(0)+1=0+1=1\\\\f(1)=\u2212(1)+1=\u22121+1=0\\\\f(2)=\u2212(2)+1=\u22122+1=\u22121[\/latex]<\/p>\r\n\r\n<table style=\"width: 20%;\">\r\n<tbody>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong><i>x<\/i><\/strong><\/td>\r\n<td style=\"text-align: center;\"><strong><i>f<\/i>(<i>x<\/i>)<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\">[latex]\u22122[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]3[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\">[latex]\u22121[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]2[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\">[latex]0[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]1[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\">[latex]1[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]0[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\">[latex]2[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]\u22121[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nPlot the points.\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/121\/2016\/04\/18232428\/image007.gif\" alt=\"The point negative 2, 3; the point negative 1, 2; the point 0, 1; the point 1, 0; the point 2, negative 1.\" width=\"322\" height=\"353\" \/>\r\n\r\nSince the points lie on a line, use a straight edge to draw the line. Try to go through each point without moving the straight edge.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/121\/2016\/04\/18232430\/image008.gif\" alt=\"Line through the points in the last graph.\" width=\"322\" height=\"353\" \/>\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nThe following video shows another example of how to graph a linear function on a set of coordinate axes.\r\n\r\nhttps:\/\/youtu.be\/sfzpdThXpA8","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Outcome<\/h3>\n<ul>\n<li>Graph linear functions using tables<\/li>\n<\/ul>\n<\/div>\n<p>A helpful first step in graphing a function is to make a table of values. This is particularly useful when you do not know the general shape the function will have. You probably already know that a linear function will be a straight line, but let us make a table first to see how it can be helpful.<\/p>\n<p>When making a table, it is a good idea to include negative values, positive values, and zero to ensure that you do have a linear function.<\/p>\n<p>Make a table of values for [latex]f(x)=3x+2[\/latex].<\/p>\n<p>Make a two-column table. Label the columns <i>x<\/i> and <i>f<\/i>(<i>x<\/i>).<\/p>\n<table style=\"width: 20%;\">\n<thead>\n<tr>\n<th style=\"text-align: center;\"><i>x<\/i><\/th>\n<th style=\"text-align: center;\"><i>f<\/i>(<i>x<\/i>)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"text-align: center;\"><\/td>\n<td style=\"text-align: center;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><\/td>\n<td style=\"text-align: center;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Choose several values for <i>x<\/i> and put them as separate rows in the <i>x<\/i> column. These are YOUR CHOICE &#8211; there is no &#8220;right&#8221; or &#8220;wrong&#8221; values to pick, just go for it.<\/p>\n<p><i>Tip:<\/i> It is always good to include 0, positive values, and negative values, if possible.<\/p>\n<table style=\"width: 20%; height: 72px;\">\n<thead>\n<tr style=\"height: 12px;\">\n<th style=\"text-align: center; height: 12px;\"><i>x<\/i><\/th>\n<th style=\"text-align: center; height: 12px;\"><i>f<\/i>(<i>x<\/i>)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr style=\"height: 12px;\">\n<td style=\"text-align: center; height: 12px;\">[latex]\u22122[\/latex]<\/td>\n<td style=\"text-align: center; height: 12px;\"><\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"text-align: center; height: 12px;\">[latex]\u22121[\/latex]<\/td>\n<td style=\"text-align: center; height: 12px;\"><\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"text-align: center; height: 12px;\">[latex]0[\/latex]<\/td>\n<td style=\"text-align: center; height: 12px;\"><\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"text-align: center; height: 12px;\">[latex]1[\/latex]<\/td>\n<td style=\"text-align: center; height: 12px;\"><\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"text-align: center; height: 12px;\">[latex]3[\/latex]<\/td>\n<td style=\"text-align: center; height: 12px;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Evaluate the function for each value of <i>x<\/i>, and write the result in the <i>f<\/i>(<i>x<\/i>) column next to the <i>x<\/i> value you used.<\/p>\n<p>When [latex]x=0[\/latex], [latex]f(0)=3(0)+2=2[\/latex],<\/p>\n<p>[latex]f(1)=3(1)+2=5[\/latex],<\/p>\n<p>[latex]f(\u22121)=3(\u22121)+2=\u22123+2=\u22121[\/latex],\u00a0and so on.<\/p>\n<table style=\"width: 20%;\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\"><strong><i>x<\/i><\/strong><\/td>\n<td style=\"text-align: center;\"><strong><i>f<\/i>(<i>x<\/i>)<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">[latex]\u22122[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]\u22124[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">[latex]\u22121[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]\u22121[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">[latex]0[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]2[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">[latex]1[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]5[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">[latex]3[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]11[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>(Note that your table of values may be different from someone else\u2019s. You may each choose different numbers for <i>x<\/i>.)<\/p>\n<p>Now that you have a table of values, you can use them to help you draw both the shape and location of the function. <i>Important:<\/i> The graph of the function will show all possible values of <i>x<\/i> and the corresponding values of <i>y<\/i>. This is why the graph is a line and not just the dots that make up the points in our table.<\/p>\n<p>Now graph [latex]f(x)=3x+2[\/latex].<br \/>\nUsing the table of values we created above, you can think of <i>f<\/i>(<i>x<\/i>) as <i>y. <\/i>Each row forms an ordered pair that you can plot on a coordinate grid.<\/p>\n<table style=\"width: 20%;\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\"><strong><i>x<\/i><\/strong><\/td>\n<td style=\"text-align: center;\"><strong><i>f<\/i>(<i>x<\/i>)<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">[latex]\u22122[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]\u22124[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">[latex]\u22121[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]\u22121[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">[latex]0[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]2[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">[latex]1[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]5[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">[latex]3[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]11[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Plot the points.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/121\/2016\/04\/18232424\/image005.gif\" alt=\"The points negative 2, negative 4; the point negative 1, negative 1; the point 0, 2; the point 1, 5; the point 3, 11.\" width=\"322\" height=\"353\" \/><\/p>\n<p>Since the points lie on a line, use a straight edge to draw the line. Try to go through each point without moving the straight edge.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/121\/2016\/04\/18232426\/image006.gif\" alt=\"A line through the points in the previous graph.\" width=\"322\" height=\"353\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>Let us try another one. Before you look at the answer, try to make the table yourself and draw the graph on a piece of paper.<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Graph [latex]f(x)=\u2212x+1[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q748367\">Show Solution<\/span><\/p>\n<div id=\"q748367\" class=\"hidden-answer\" style=\"display: none\">\n<p>Start with a table of values. You can choose different values for <i>x<\/i>, but once again, it is helpful to include [latex]0[\/latex], some positive values, and some negative values.<\/p>\n<p>If you think of <i>f<\/i>(<i>x<\/i>) as <i>y,<\/i> each row forms an ordered pair that you can plot on a coordinate grid.<\/p>\n<p style=\"text-align: center;\">[latex]f(\u22122)=\u2212(\u22122)+1=2+1=3\\\\f(\u22121)=\u2212(\u22121)+1=1+1=2\\\\f(0)=\u2212(0)+1=0+1=1\\\\f(1)=\u2212(1)+1=\u22121+1=0\\\\f(2)=\u2212(2)+1=\u22122+1=\u22121[\/latex]<\/p>\n<table style=\"width: 20%;\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\"><strong><i>x<\/i><\/strong><\/td>\n<td style=\"text-align: center;\"><strong><i>f<\/i>(<i>x<\/i>)<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">[latex]\u22122[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]3[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">[latex]\u22121[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]2[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">[latex]0[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]1[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">[latex]1[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]0[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">[latex]2[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]\u22121[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Plot the points.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/121\/2016\/04\/18232428\/image007.gif\" alt=\"The point negative 2, 3; the point negative 1, 2; the point 0, 1; the point 1, 0; the point 2, negative 1.\" width=\"322\" height=\"353\" \/><\/p>\n<p>Since the points lie on a line, use a straight edge to draw the line. Try to go through each point without moving the straight edge.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/121\/2016\/04\/18232430\/image008.gif\" alt=\"Line through the points in the last graph.\" width=\"322\" height=\"353\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>The following video shows another example of how to graph a linear function on a set of coordinate axes.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex: Graph a Linear Function Using a Table of Values (Function Notation)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/sfzpdThXpA8?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-163\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Revision and Adaptation. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Ex: Graph a Linear Function Using a Table of Values (Function Notation). <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) . <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/sfzpdThXpA8\">https:\/\/youtu.be\/sfzpdThXpA8<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Unit 17: Functions, from Developmental Math: An Open Program. . <strong>Provided by<\/strong>: Monterey Institute of Technology and Education. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/nrocnetwork.org\/dm-opentext\">http:\/\/nrocnetwork.org\/dm-opentext<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":395986,"menu_order":3,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Ex: Graph a Linear Function Using a Table of Values (Function Notation)\",\"author\":\"James Sousa (Mathispower4u.com) \",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/sfzpdThXpA8\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen 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