{"id":40,"date":"2025-02-13T22:43:04","date_gmt":"2025-02-13T22:43:04","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/precalculus\/chapter\/determine-whether-a-relation-represents-a-function\/"},"modified":"2025-12-17T16:21:03","modified_gmt":"2025-12-17T16:21:03","slug":"determine-whether-a-relation-represents-a-function","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/precalculus\/chapter\/determine-whether-a-relation-represents-a-function\/","title":{"raw":"Functions and Function Notation: Learn It 1","rendered":"Functions and Function Notation: Learn It 1"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\"><section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\r\n<ul>\r\n \t<li>Understand what a function is and use the vertical line test to check if a graph shows a function<\/li>\r\n \t<li>Use function notation [latex]f(x)[\/latex] and evaluate functions<\/li>\r\n \t<li>Recognize the graphs of common functions<\/li>\r\n<\/ul>\r\n<\/section><\/div>\r\n<h2>Determining Whether a Relation is a Function<\/h2>\r\n<p id=\"fs-id1165137431376\">A jetliner changes altitude as its distance from the starting point of a flight increases. The weight of a growing child increases with time. In each case, one quantity depends on another. There is a relationship between the two quantities that we can describe, analyze, and use to make predictions. In this section, we will analyze such relationships.<\/p>\r\nA\u00a0<strong><span id=\"term-00005\" data-type=\"term\">relation<\/span><\/strong>\u00a0is a set of ordered pairs. The set of the first components of each\u00a0ordered pair\u00a0is called the\u00a0<strong>domain\u00a0<\/strong>and the set of the second components of each ordered pair is called the\u00a0<strong>range<\/strong>. Note that each value in the domain is also known as an\u00a0<strong>input<\/strong>\u00a0value, or\u00a0<strong>independent variable<\/strong>, and is often labeled with the lowercase letter [latex]x[\/latex]. Each value in the range is also known as an <strong>output<\/strong>\u00a0value, or\u00a0<strong>dependent variable<\/strong>, and is often labeled with lowercase letter [latex]y[\/latex].\r\n\r\n<section class=\"textbox keyTakeaway\">\r\n<h3>relation, domain, and range<\/h3>\r\nA <strong>relation<\/strong> is defined as a set of ordered pairs, where the set of first components is known as the <strong>domain<\/strong> and each value in it is an input or independent variable, often labeled [latex]x[\/latex]. The set of second components in the ordered pairs is called the <strong>range<\/strong>, and each value in the range is an output or dependent variable, often labeled [latex]y[\/latex].\r\n\r\n<\/section>\r\n<h2>Determining Whether a Relation Represents a Function<\/h2>\r\nConsider the following set of ordered pairs.\r\n<div id=\"fs-id1165137676332\" class=\"equation unnumbered\" style=\"text-align: center;\">[latex]\\begin{gather}\\left\\{\\left(1,2\\right),\\left(2,4\\right),\\left(3,6\\right),\\left(4,8\\right),\\left(5,10\\right)\\right\\}\\\\{ } \\end{gather}[\/latex]<\/div>\r\n<p id=\"fs-id1165133155834\">The domain is [latex]\\left\\{1,2,3,4,5\\right\\}[\/latex].\u00a0The range is [latex]\\left\\{2,4,6,8,10\\right\\}[\/latex].<\/p>\r\n<p id=\"fs-id1165134234609\">Note that each value in the domain is also known as an <strong>input<\/strong> value. The input values are values of the\u00a0<strong>independent variable<\/strong>\u00a0which often labeled with the lowercase letter [latex]x[\/latex]. Each value in the range is also known as an <strong>output<\/strong> value. The output values are values of the\u00a0<strong>dependent variable<\/strong>\u00a0which is often labeled lowercase letter [latex]y[\/latex].<\/p>\r\n<p id=\"fs-id1165137748300\">A <strong>function<\/strong> [latex]f[\/latex] is a relation that assigns a single value in the range to each value in the domain<em>.<\/em> In other words no [latex]x[\/latex]-values are repeated.<\/p>\r\n\r\n<section class=\"textbox keyTakeaway\">\r\n<h3>function<\/h3>\r\nA <strong>function<\/strong> is a specific type of relation where each input value corresponds to one and only one output value. We say \u201cthe output is a function of the input.\u201d\r\n\r\n&nbsp;\r\n\r\nIn a function:\r\n<ul>\r\n \t<li>The input values make up the domain<\/li>\r\n \t<li>The output values make up the range.<\/li>\r\n \t<li>The input value is called the independent value.<\/li>\r\n \t<li>The output value is called the dependent value because it depends on the input value.<\/li>\r\n<\/ul>\r\n<\/section>\r\n<p id=\"fs-id1165135421564\">Now let\u2019s consider the set of ordered pairs that relates the terms \"even\" and \"odd\" to the first five natural numbers. It would appear as<\/p>\r\n\r\n<div id=\"fs-id1165133192963\" class=\"equation unnumbered\" style=\"text-align: center;\">[latex]\\begin{gather}\\left\\{\\left(\\text{odd},1\\right),\\left(\\text{even},2\\right),\\left(\\text{odd},3\\right),\\left(\\text{even},4\\right),\\left(\\text{odd},5\\right)\\right\\}\\\\{ }\\end{gather}[\/latex]<\/div>\r\n<div><\/div>\r\n<p id=\"fs-id1165135419796\">Notice that each element in the domain, [latex]\\left\\{\\text{even,}\\text{odd}\\right\\}[\/latex]\u00a0is <em>not<\/em> paired with exactly one element in the range, [latex]\\left\\{1,2,3,4,5\\right\\}[\/latex].\u00a0For example, the term \"odd\" corresponds to three values from the domain, [latex]\\left\\{1,3,5\\right\\}[\/latex]\u00a0and the term \"even\" corresponds to two values from the range, [latex]\\left\\{2,4\\right\\}[\/latex].\u00a0This violates the definition of a function, so this relation is not a function.<\/p>\r\nThe figure below compares relations that are functions and not functions.\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"975\"]<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03010531\/CNX_Precalc_Figure_01_01_0012.jpg\" alt=\"Three relations that demonstrate what constitute a function.\" width=\"975\" height=\"243\" \/> (a) This relationship is a function because each input is associated with a single output. Note that input [latex]q[\/latex] and [latex]r[\/latex] both give output [latex]n[\/latex]. (b) This relationship is also a function. In this case, each input is associated with a single output. (c) This relationship is not a function because input [latex]q[\/latex] is associated with two different outputs.[\/caption]<section class=\"textbox example\" aria-label=\"Example\">\r\n<p id=\"fs-id1165137436464\">The coffee shop menu consists of items and their prices.<\/p>\r\n\r\n<ol id=\"fs-id1165137646341\">\r\n \t<li>Is price a function of the item?<\/li>\r\n \t<li>Is the item a function of the price?<\/li>\r\n<\/ol>\r\n&nbsp;\r\n<figure id=\"Figure_01_01_004\" class=\"small\"><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03010531\/CNX_Precalc_Figure_01_01_0042.jpg\" alt=\"A menu of donut prices from a coffee shop where a plain donut is $1.49 and a jelly donut and chocolate donut are $1.99.\" width=\"487\" height=\"233\" \/><\/figure>\r\n<h3><\/h3>\r\n[reveal-answer q=\"737169\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"737169\"]\r\n<ol id=\"fs-id1165137643241\">\r\n \t<li>Let\u2019s begin by considering the input as the items on the menu. The output values are then the prices.\r\n<figure id=\"Figure_01_01_027\" class=\"medium\"><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03010531\/CNX_Precalc_Figure_01_01_0272.jpg\" alt=\"A menu of donut prices from a coffee shop where a plain donut is $1.49 and a jelly donut and chocolate donut are $1.99.\" width=\"731\" height=\"241\" \/><\/figure>\r\n<p id=\"fs-id1165135532324\">Each item on the menu has only one price, so the price is a function of the item.<\/p>\r\n<\/li>\r\n \t<li>Two items on the menu have the same price. If we consider the prices to be the input values and the items to be the output, then the same input value could have more than one output associated with it.\r\n<figure id=\"Figure_01_01_028\" class=\"medium\"><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03010531\/CNX_Precalc_Figure_01_01_0282.jpg\" alt=\"Association of the prices to the donuts.\" width=\"731\" height=\"241\" \/><\/figure>\r\n<p id=\"fs-id1165137754835\">Therefore, the item is a not a function of price.<\/p>\r\n<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n<\/section><section class=\"textbox example\" aria-label=\"Example\">In a particular math class, the overall percent grade corresponds to a grade point average. Is grade point average a function of the percent grade? Is the percent grade a function of the grade point average? The table below shows a possible rule for assigning grade points.\r\n<table>\r\n<tbody>\r\n<tr>\r\n<th>Percent Grade<\/th>\r\n<td>0\u201356<\/td>\r\n<td>57\u201361<\/td>\r\n<td>62\u201366<\/td>\r\n<td>67\u201371<\/td>\r\n<td>72\u201377<\/td>\r\n<td>78\u201386<\/td>\r\n<td>87\u201391<\/td>\r\n<td>92\u2013100<\/td>\r\n<\/tr>\r\n<tr>\r\n<th>Grade Point Average<\/th>\r\n<td>0.0<\/td>\r\n<td>1.0<\/td>\r\n<td>1.5<\/td>\r\n<td>2.0<\/td>\r\n<td>2.5<\/td>\r\n<td>3.0<\/td>\r\n<td>3.5<\/td>\r\n<td>4.0<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[reveal-answer q=\"362965\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"362965\"]\r\n<p id=\"fs-id1165135260743\">For any percent grade earned, there is an associated grade point average, so the grade point average is a function of the percent grade. In other words, if we input the percent grade, the output is a specific grade point average.<\/p>\r\n<p id=\"fs-id1165137807321\">In the grading system given, there is a range of percent grades that correspond to the same grade point average. For example, students who receive a grade point average of 3.0 could have a variety of percent grades ranging from 78 all the way to 86. Thus, percent grade is not a function of grade point average.<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<div id=\"ti_01_01_01\" class=\"exercise\">\r\n<div id=\"fs-id1165135667843\" class=\"problem\">\r\n<div class=\"bcc-box bcc-success\">\r\n<p id=\"fs-id1165137627634\">[ohm_question hide_question_numbers=1]317457[\/ohm_question]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/section>\r\n<div id=\"Example_01_01_02\" class=\"example\">\r\n<div id=\"fs-id1165137437773\" class=\"exercise\">\r\n<div id=\"fs-id1165137588587\" class=\"note precalculus try\">\r\n<div id=\"fs-id1165137588587\" class=\"note precalculus try\">\r\n<div id=\"ti_01_01_01\" class=\"exercise\">\r\n<div id=\"fs-id1165135667843\" class=\"problem\"><section id=\"fs-id1165137804204\">\r\n<div id=\"Example_01_01_05\" class=\"example\">\r\n<div id=\"fs-id1165137416794\" class=\"exercise\"><section id=\"fs-id1165137648450\">\r\n<div class=\"bcc-box bcc-success\"><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]19056[\/ohm2_question]<\/section><\/div>\r\n<section aria-label=\"Try It\"><\/section><\/section><\/div>\r\n<\/div>\r\n<\/section>\r\n<div><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>","rendered":"<div class=\"bcc-box bcc-highlight\">\n<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\n<ul>\n<li>Understand what a function is and use the vertical line test to check if a graph shows a function<\/li>\n<li>Use function notation [latex]f(x)[\/latex] and evaluate functions<\/li>\n<li>Recognize the graphs of common functions<\/li>\n<\/ul>\n<\/section>\n<\/div>\n<h2>Determining Whether a Relation is a Function<\/h2>\n<p id=\"fs-id1165137431376\">A jetliner changes altitude as its distance from the starting point of a flight increases. The weight of a growing child increases with time. In each case, one quantity depends on another. There is a relationship between the two quantities that we can describe, analyze, and use to make predictions. In this section, we will analyze such relationships.<\/p>\n<p>A\u00a0<strong><span id=\"term-00005\" data-type=\"term\">relation<\/span><\/strong>\u00a0is a set of ordered pairs. The set of the first components of each\u00a0ordered pair\u00a0is called the\u00a0<strong>domain\u00a0<\/strong>and the set of the second components of each ordered pair is called the\u00a0<strong>range<\/strong>. Note that each value in the domain is also known as an\u00a0<strong>input<\/strong>\u00a0value, or\u00a0<strong>independent variable<\/strong>, and is often labeled with the lowercase letter [latex]x[\/latex]. Each value in the range is also known as an <strong>output<\/strong>\u00a0value, or\u00a0<strong>dependent variable<\/strong>, and is often labeled with lowercase letter [latex]y[\/latex].<\/p>\n<section class=\"textbox keyTakeaway\">\n<h3>relation, domain, and range<\/h3>\n<p>A <strong>relation<\/strong> is defined as a set of ordered pairs, where the set of first components is known as the <strong>domain<\/strong> and each value in it is an input or independent variable, often labeled [latex]x[\/latex]. The set of second components in the ordered pairs is called the <strong>range<\/strong>, and each value in the range is an output or dependent variable, often labeled [latex]y[\/latex].<\/p>\n<\/section>\n<h2>Determining Whether a Relation Represents a Function<\/h2>\n<p>Consider the following set of ordered pairs.<\/p>\n<div id=\"fs-id1165137676332\" class=\"equation unnumbered\" style=\"text-align: center;\">[latex]\\begin{gather}\\left\\{\\left(1,2\\right),\\left(2,4\\right),\\left(3,6\\right),\\left(4,8\\right),\\left(5,10\\right)\\right\\}\\\\{ } \\end{gather}[\/latex]<\/div>\n<p id=\"fs-id1165133155834\">The domain is [latex]\\left\\{1,2,3,4,5\\right\\}[\/latex].\u00a0The range is [latex]\\left\\{2,4,6,8,10\\right\\}[\/latex].<\/p>\n<p id=\"fs-id1165134234609\">Note that each value in the domain is also known as an <strong>input<\/strong> value. The input values are values of the\u00a0<strong>independent variable<\/strong>\u00a0which often labeled with the lowercase letter [latex]x[\/latex]. Each value in the range is also known as an <strong>output<\/strong> value. The output values are values of the\u00a0<strong>dependent variable<\/strong>\u00a0which is often labeled lowercase letter [latex]y[\/latex].<\/p>\n<p id=\"fs-id1165137748300\">A <strong>function<\/strong> [latex]f[\/latex] is a relation that assigns a single value in the range to each value in the domain<em>.<\/em> In other words no [latex]x[\/latex]-values are repeated.<\/p>\n<section class=\"textbox keyTakeaway\">\n<h3>function<\/h3>\n<p>A <strong>function<\/strong> is a specific type of relation where each input value corresponds to one and only one output value. We say \u201cthe output is a function of the input.\u201d<\/p>\n<p>&nbsp;<\/p>\n<p>In a function:<\/p>\n<ul>\n<li>The input values make up the domain<\/li>\n<li>The output values make up the range.<\/li>\n<li>The input value is called the independent value.<\/li>\n<li>The output value is called the dependent value because it depends on the input value.<\/li>\n<\/ul>\n<\/section>\n<p id=\"fs-id1165135421564\">Now let\u2019s consider the set of ordered pairs that relates the terms &#8220;even&#8221; and &#8220;odd&#8221; to the first five natural numbers. It would appear as<\/p>\n<div id=\"fs-id1165133192963\" class=\"equation unnumbered\" style=\"text-align: center;\">[latex]\\begin{gather}\\left\\{\\left(\\text{odd},1\\right),\\left(\\text{even},2\\right),\\left(\\text{odd},3\\right),\\left(\\text{even},4\\right),\\left(\\text{odd},5\\right)\\right\\}\\\\{ }\\end{gather}[\/latex]<\/div>\n<div><\/div>\n<p id=\"fs-id1165135419796\">Notice that each element in the domain, [latex]\\left\\{\\text{even,}\\text{odd}\\right\\}[\/latex]\u00a0is <em>not<\/em> paired with exactly one element in the range, [latex]\\left\\{1,2,3,4,5\\right\\}[\/latex].\u00a0For example, the term &#8220;odd&#8221; corresponds to three values from the domain, [latex]\\left\\{1,3,5\\right\\}[\/latex]\u00a0and the term &#8220;even&#8221; corresponds to two values from the range, [latex]\\left\\{2,4\\right\\}[\/latex].\u00a0This violates the definition of a function, so this relation is not a function.<\/p>\n<p>The figure below compares relations that are functions and not functions.<\/p>\n<figure style=\"width: 975px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03010531\/CNX_Precalc_Figure_01_01_0012.jpg\" alt=\"Three relations that demonstrate what constitute a function.\" width=\"975\" height=\"243\" \/><figcaption class=\"wp-caption-text\">(a) This relationship is a function because each input is associated with a single output. Note that input [latex]q[\/latex] and [latex]r[\/latex] both give output [latex]n[\/latex]. (b) This relationship is also a function. In this case, each input is associated with a single output. (c) This relationship is not a function because input [latex]q[\/latex] is associated with two different outputs.<\/figcaption><\/figure>\n<section class=\"textbox example\" aria-label=\"Example\">\n<p id=\"fs-id1165137436464\">The coffee shop menu consists of items and their prices.<\/p>\n<ol id=\"fs-id1165137646341\">\n<li>Is price a function of the item?<\/li>\n<li>Is the item a function of the price?<\/li>\n<\/ol>\n<p>&nbsp;<\/p>\n<figure id=\"Figure_01_01_004\" class=\"small\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03010531\/CNX_Precalc_Figure_01_01_0042.jpg\" alt=\"A menu of donut prices from a coffee shop where a plain donut is $1.49 and a jelly donut and chocolate donut are $1.99.\" width=\"487\" height=\"233\" \/><\/figure>\n<h3><\/h3>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q737169\">Show Solution<\/button><\/p>\n<div id=\"q737169\" class=\"hidden-answer\" style=\"display: none\">\n<ol id=\"fs-id1165137643241\">\n<li>Let\u2019s begin by considering the input as the items on the menu. The output values are then the prices.<br \/>\n<figure id=\"Figure_01_01_027\" class=\"medium\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03010531\/CNX_Precalc_Figure_01_01_0272.jpg\" alt=\"A menu of donut prices from a coffee shop where a plain donut is $1.49 and a jelly donut and chocolate donut are $1.99.\" width=\"731\" height=\"241\" \/><\/figure>\n<p id=\"fs-id1165135532324\">Each item on the menu has only one price, so the price is a function of the item.<\/p>\n<\/li>\n<li>Two items on the menu have the same price. If we consider the prices to be the input values and the items to be the output, then the same input value could have more than one output associated with it.<br \/>\n<figure id=\"Figure_01_01_028\" class=\"medium\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03010531\/CNX_Precalc_Figure_01_01_0282.jpg\" alt=\"Association of the prices to the donuts.\" width=\"731\" height=\"241\" \/><\/figure>\n<p id=\"fs-id1165137754835\">Therefore, the item is a not a function of price.<\/p>\n<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox example\" aria-label=\"Example\">In a particular math class, the overall percent grade corresponds to a grade point average. Is grade point average a function of the percent grade? Is the percent grade a function of the grade point average? The table below shows a possible rule for assigning grade points.<\/p>\n<table>\n<tbody>\n<tr>\n<th>Percent Grade<\/th>\n<td>0\u201356<\/td>\n<td>57\u201361<\/td>\n<td>62\u201366<\/td>\n<td>67\u201371<\/td>\n<td>72\u201377<\/td>\n<td>78\u201386<\/td>\n<td>87\u201391<\/td>\n<td>92\u2013100<\/td>\n<\/tr>\n<tr>\n<th>Grade Point Average<\/th>\n<td>0.0<\/td>\n<td>1.0<\/td>\n<td>1.5<\/td>\n<td>2.0<\/td>\n<td>2.5<\/td>\n<td>3.0<\/td>\n<td>3.5<\/td>\n<td>4.0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q362965\">Show Solution<\/button><\/p>\n<div id=\"q362965\" class=\"hidden-answer\" style=\"display: none\">\n<p id=\"fs-id1165135260743\">For any percent grade earned, there is an associated grade point average, so the grade point average is a function of the percent grade. In other words, if we input the percent grade, the output is a specific grade point average.<\/p>\n<p id=\"fs-id1165137807321\">In the grading system given, there is a range of percent grades that correspond to the same grade point average. For example, students who receive a grade point average of 3.0 could have a variety of percent grades ranging from 78 all the way to 86. Thus, percent grade is not a function of grade point average.<\/p>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<div id=\"ti_01_01_01\" class=\"exercise\">\n<div id=\"fs-id1165135667843\" class=\"problem\">\n<div class=\"bcc-box bcc-success\">\n<p id=\"fs-id1165137627634\"><iframe loading=\"lazy\" id=\"ohm317457\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=317457&theme=lumen&iframe_resize_id=ohm317457&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<div id=\"Example_01_01_02\" class=\"example\">\n<div id=\"fs-id1165137437773\" class=\"exercise\">\n<div id=\"fs-id1165137588587\" class=\"note precalculus try\">\n<div class=\"note precalculus try\">\n<div class=\"exercise\">\n<div class=\"problem\">\n<section id=\"fs-id1165137804204\">\n<div id=\"Example_01_01_05\" class=\"example\">\n<div id=\"fs-id1165137416794\" class=\"exercise\">\n<section id=\"fs-id1165137648450\">\n<div class=\"bcc-box bcc-success\">\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm19056\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=19056&theme=lumen&iframe_resize_id=ohm19056&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<\/div>\n<section aria-label=\"Try It\"><\/section>\n<\/section>\n<\/div>\n<\/div>\n<\/section>\n<div><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"author":6,"menu_order":6,"template":"","meta":{"_candela_citation":"[{\"type\":\"copyrighted_video\",\"description\":\"Determine if a Relation is a Function\",\"author\":\"James Sousa\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/zT69oxcMhPw\",\"project\":\"\",\"license\":\"arr\",\"license_terms\":\"Standard YouTube License\"},{\"type\":\"cc\",\"description\":\"Function Notation Application\",\"author\":\"James 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