{"id":189,"date":"2024-10-18T21:12:55","date_gmt":"2024-10-18T21:12:55","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/chapter\/function-basics-learn-it-1\/"},"modified":"2024-10-18T21:12:55","modified_gmt":"2024-10-18T21:12:55","slug":"function-basics-learn-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/chapter\/function-basics-learn-it-1\/","title":{"raw":"Function Basics: Learn It 1","rendered":"Function Basics: Learn It 1"},"content":{"raw":"\n<section class=\"textbox learningGoals\">\n<ul>\n\t<li>Define what a function is and apply the vertical line test to identify functions<\/li>\n\t<li>Use function notation to represent and evaluate functions<\/li>\n\t<li>Recognize the graphs of fundamental toolkit functions<\/li>\n<\/ul>\n<\/section>\n<h2 data-type=\"title\">Determining Whether a Relation Represents a Function<\/h2>\n<p>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&nbsp;<strong><span id=\"term-00005\" data-type=\"term\">relation<\/span><\/strong>&nbsp;is a set of ordered pairs. The set of the first components of each&nbsp;ordered pair&nbsp;is called the&nbsp;<strong>domain&nbsp;<\/strong>and the set of the second components of each ordered pair is called the&nbsp;<strong>range<\/strong>. Note that each value in the domain is also known as an&nbsp;<strong>input<\/strong>&nbsp;value, or&nbsp;<strong>independent variable<\/strong>, and is often labeled with the lowercase letter [latex]x[\/latex]&nbsp;Each value in the range is also known as an&nbsp;<strong>output<\/strong>&nbsp;value, or&nbsp;<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<p>Consider the following set of ordered pairs. The first numbers in each pair are the first five natural numbers. The second number in each pair is twice that of the first.<\/p>\n<p style=\"text-align: center;\">[latex]\\{(1,2),(2,4),(3,6),(4,8),(5,10)\\}[\/latex]<\/p>\n<p>The domain is [latex]\\{1,2,3,4,5\\}[\/latex]. The range is [latex]\\{2,4,6,8,10\\}[\/latex].<\/p>\n<p>A <strong>function<\/strong> [latex]f[\/latex] is a relation that assigns a single value in the range to each value in the domain. 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 relation in which each possible input value leads to exactly one output value. We say \u201cthe output is a function of the input.\u201d<\/p>\n<p>&nbsp;<\/p>\n<p>The <strong>input <\/strong>values make up the <strong>domain<\/strong>, and the <strong>output <\/strong>values make up the <strong>range<\/strong>.<\/p>\n<\/section>\n<p>For our example that relates the first five natural numbers to numbers double their values, this relation is a function because each element in the domain, [latex]\\{1,2,3,4,5\\}[\/latex], is paired with exactly one element in the range, [latex]\\{2,4,6,8,10\\}[\/latex].<\/p>\n<p>Now let\u2019s consider the set of ordered pairs that relates the terms \u201ceven\u201d and \u201codd\u201d to the first five natural numbers. It would appear as<\/p>\n<p style=\"text-align: center;\">[latex]\\{(odd,1),(even,2),(odd,3),(even,4),(odd,5)\\}[\/latex]<\/p>\n<p>Notice that each element in the domain, [latex]\\{even,odd\\}[\/latex] is not paired with exactly one element in the range, [latex]\\{1,2,3,4,5\\}[\/latex]. For example, the term \u201codd\u201d corresponds to three values from the range, [latex]\\{1,3,5\\}[\/latex] and the term \u201ceven\u201d corresponds to two values from the range, [latex]\\{2,4\\}[\/latex]. This 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<center><img class=\"wp-image-9157 size-full\" src=\"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-content\/uploads\/sites\/18\/2023\/10\/6b41ee83a62edd93cf9e80894490f065d2031df7.png#fixme\" alt=\"Three relations that demonstrate what constitute a function.\" width=\"943\" height=\"284\"><\/center><center><strong><span style=\"font-size: 10pt;\">(a) This relationship is a function because each input is associated with a single output.<\/span><\/strong><strong><span style=\"font-size: 10pt;\">Note that input [latex]q[\/latex] and [latex]r[\/latex] both give output [latex]n[\/latex]. <\/span><\/strong><\/center><center><strong><span style=\"font-size: 10pt;\">(b) This relationship is also a function. In this case, each input is associated with a single output. <\/span><\/strong><\/center><center><strong><span style=\"font-size: 10pt;\">(c) This relationship is not a function because input [latex]q[\/latex] is associated with two different outputs.<\/span><\/strong><\/center>\n<p>&nbsp;<\/p>\n<section class=\"textbox questionHelp\">\n<p id=\"fs-id1165137635406\"><strong>How to: Given a relationship between two quantities, determine whether the relationship is a function.<\/strong><\/p>\n<ol id=\"fs-id1165134065124\" type=\"1\">\n\t<li>Identify the input values.<\/li>\n\t<li>Identify the output values.<\/li>\n\t<li>If each input value leads to only one output value, classify the relationship as a function. If any input value leads to two or more outputs, do not classify the relationship as a function.<\/li>\n<\/ol>\n<\/section>\n<section class=\"textbox example\">In a particular math class, the overall percent grade corresponds to a grade point average. The table below shows a possible rule for assigning grade points.\n\n<ol style=\"list-style-type: lower-alpha;\">\n\t<li>Is grade point average a function of the percent grade?<\/li>\n\t<li>Is the percent grade a function of the grade point average?<\/li>\n<\/ol>\n<table border=\"1\">\n<thead>\n<tr>\n<th style=\"width: 5%;\">Percent grade<\/th>\n<th>[latex]0\u201356[\/latex]<\/th>\n<th>[latex]57\u201361[\/latex]<\/th>\n<th>[latex]62\u201366[\/latex]<\/th>\n<th>[latex]67\u201371[\/latex]<\/th>\n<th>[latex]72\u201377[\/latex]<\/th>\n<th>[latex]78\u201386[\/latex]<\/th>\n<th>[latex]87\u201391[\/latex]<\/th>\n<th>[latex]92\u2013100[\/latex]<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"width: 5%;\">Grade point average<\/td>\n<td>[latex]0.0[\/latex]<\/td>\n<td>[latex]1.0[\/latex]<\/td>\n<td>[latex]1.5[\/latex]<\/td>\n<td>[latex]2.0[\/latex]<\/td>\n<td>[latex]2.5[\/latex]<\/td>\n<td>[latex]3.0[\/latex]<\/td>\n<td>[latex]3.5[\/latex]<\/td>\n<td>[latex]4.0[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n[reveal-answer q=\"214538\"]Show Solution[\/reveal-answer] [hidden-answer a=\"214538\"]\n\n<ol style=\"list-style-type: lower-alpha;\">\n\t<li>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.<\/li>\n\t<li>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 [latex]3.0[\/latex] could have a variety of percent grades ranging from [latex]78[\/latex] all the way to [latex]86[\/latex]. Thus, percent grade is not a function of grade point average.<\/li>\n<\/ol>\n\n[\/hidden-answer]<\/section>\n<section class=\"textbox example\">Define the domain and range for the following set of ordered pairs, and determine whether the relation given is a function.\n\n<p style=\"text-align: center;\">[latex]\\{(\u22123,\u22126),(\u22122,\u22121),(1,0),(1,5),(2,0)\\}[\/latex]<\/p>\n\n[reveal-answer q=\"507050\"]Show Solution[\/reveal-answer] [hidden-answer a=\"507050\"] We list all of the input values as the domain. &nbsp;The input values are represented first in the ordered pair as a matter of convention. <br>\n<br>\nDomain: {[latex]-3,-2,1,2[\/latex]} <br>\n<br>\nNote how we did not enter repeated values more than once; it is not necessary. <br>\n<br>\nThe range is the list of outputs for the relation; they are entered second in the ordered pair. <br>\n<br>\nRange: {[latex]-6, -1, 0, 5[\/latex]} <br>\n<br>\n<p>Organizing the ordered pairs in a table can help you tell whether this relation is a function. &nbsp;By definition, the inputs in a function have only one output.<\/p>\n<center>\n<table style=\"width: 50%;\">\n<tbody>\n<tr>\n<th style=\"text-align: center;\" scope=\"row\"><i>x<\/i><\/th>\n<th style=\"text-align: center;\"><i>y<\/i><\/th>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" scope=\"row\">[latex]\u22123[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]\u22126[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" scope=\"row\">[latex]\u22122[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]\u22121[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" scope=\"row\">[latex]1[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]0[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" scope=\"row\">[latex]1[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]5[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" scope=\"row\">[latex]2[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]0[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/center>\n<p>&nbsp;<\/p>\n<p>The relation is not a function because the input [latex]1[\/latex] has two outputs: [latex]0[\/latex] and [latex]5[\/latex].<\/p>\n\n[\/hidden-answer]<\/section>\n<section class=\"textbox tryIt\">\n<p>[ohm2_question hide_question_numbers=1]13501[\/ohm2_question]<\/p>\n<\/section>\n","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Define what a function is and apply the vertical line test to identify functions<\/li>\n<li>Use function notation to represent and evaluate functions<\/li>\n<li>Recognize the graphs of fundamental toolkit functions<\/li>\n<\/ul>\n<\/section>\n<h2 data-type=\"title\">Determining Whether a Relation Represents a Function<\/h2>\n<p>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&nbsp;<strong><span id=\"term-00005\" data-type=\"term\">relation<\/span><\/strong>&nbsp;is a set of ordered pairs. The set of the first components of each&nbsp;ordered pair&nbsp;is called the&nbsp;<strong>domain&nbsp;<\/strong>and the set of the second components of each ordered pair is called the&nbsp;<strong>range<\/strong>. Note that each value in the domain is also known as an&nbsp;<strong>input<\/strong>&nbsp;value, or&nbsp;<strong>independent variable<\/strong>, and is often labeled with the lowercase letter [latex]x[\/latex]&nbsp;Each value in the range is also known as an&nbsp;<strong>output<\/strong>&nbsp;value, or&nbsp;<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<p>Consider the following set of ordered pairs. The first numbers in each pair are the first five natural numbers. The second number in each pair is twice that of the first.<\/p>\n<p style=\"text-align: center;\">[latex]\\{(1,2),(2,4),(3,6),(4,8),(5,10)\\}[\/latex]<\/p>\n<p>The domain is [latex]\\{1,2,3,4,5\\}[\/latex]. The range is [latex]\\{2,4,6,8,10\\}[\/latex].<\/p>\n<p>A <strong>function<\/strong> [latex]f[\/latex] is a relation that assigns a single value in the range to each value in the domain. 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 relation in which each possible input value leads to exactly one output value. We say \u201cthe output is a function of the input.\u201d<\/p>\n<p>&nbsp;<\/p>\n<p>The <strong>input <\/strong>values make up the <strong>domain<\/strong>, and the <strong>output <\/strong>values make up the <strong>range<\/strong>.<\/p>\n<\/section>\n<p>For our example that relates the first five natural numbers to numbers double their values, this relation is a function because each element in the domain, [latex]\\{1,2,3,4,5\\}[\/latex], is paired with exactly one element in the range, [latex]\\{2,4,6,8,10\\}[\/latex].<\/p>\n<p>Now let\u2019s consider the set of ordered pairs that relates the terms \u201ceven\u201d and \u201codd\u201d to the first five natural numbers. It would appear as<\/p>\n<p style=\"text-align: center;\">[latex]\\{(odd,1),(even,2),(odd,3),(even,4),(odd,5)\\}[\/latex]<\/p>\n<p>Notice that each element in the domain, [latex]\\{even,odd\\}[\/latex] is not paired with exactly one element in the range, [latex]\\{1,2,3,4,5\\}[\/latex]. For example, the term \u201codd\u201d corresponds to three values from the range, [latex]\\{1,3,5\\}[\/latex] and the term \u201ceven\u201d corresponds to two values from the range, [latex]\\{2,4\\}[\/latex]. This 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<div style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-9157 size-full\" src=\"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-content\/uploads\/sites\/18\/2023\/10\/6b41ee83a62edd93cf9e80894490f065d2031df7.png#fixme\" alt=\"Three relations that demonstrate what constitute a function.\" width=\"943\" height=\"284\" \/><\/div>\n<div style=\"text-align: center;\"><strong><span style=\"font-size: 10pt;\">(a) This relationship is a function because each input is associated with a single output.<\/span><\/strong><strong><span style=\"font-size: 10pt;\">Note that input [latex]q[\/latex] and [latex]r[\/latex] both give output [latex]n[\/latex]. <\/span><\/strong><\/div>\n<div style=\"text-align: center;\"><strong><span style=\"font-size: 10pt;\">(b) This relationship is also a function. In this case, each input is associated with a single output. <\/span><\/strong><\/div>\n<div style=\"text-align: center;\"><strong><span style=\"font-size: 10pt;\">(c) This relationship is not a function because input [latex]q[\/latex] is associated with two different outputs.<\/span><\/strong><\/div>\n<p>&nbsp;<\/p>\n<section class=\"textbox questionHelp\">\n<p id=\"fs-id1165137635406\"><strong>How to: Given a relationship between two quantities, determine whether the relationship is a function.<\/strong><\/p>\n<ol id=\"fs-id1165134065124\" type=\"1\">\n<li>Identify the input values.<\/li>\n<li>Identify the output values.<\/li>\n<li>If each input value leads to only one output value, classify the relationship as a function. If any input value leads to two or more outputs, do not classify the relationship as a function.<\/li>\n<\/ol>\n<\/section>\n<section class=\"textbox example\">In a particular math class, the overall percent grade corresponds to a grade point average. The table below shows a possible rule for assigning grade points.<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>Is grade point average a function of the percent grade?<\/li>\n<li>Is the percent grade a function of the grade point average?<\/li>\n<\/ol>\n<table>\n<thead>\n<tr>\n<th style=\"width: 5%;\">Percent grade<\/th>\n<th>[latex]0\u201356[\/latex]<\/th>\n<th>[latex]57\u201361[\/latex]<\/th>\n<th>[latex]62\u201366[\/latex]<\/th>\n<th>[latex]67\u201371[\/latex]<\/th>\n<th>[latex]72\u201377[\/latex]<\/th>\n<th>[latex]78\u201386[\/latex]<\/th>\n<th>[latex]87\u201391[\/latex]<\/th>\n<th>[latex]92\u2013100[\/latex]<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"width: 5%;\">Grade point average<\/td>\n<td>[latex]0.0[\/latex]<\/td>\n<td>[latex]1.0[\/latex]<\/td>\n<td>[latex]1.5[\/latex]<\/td>\n<td>[latex]2.0[\/latex]<\/td>\n<td>[latex]2.5[\/latex]<\/td>\n<td>[latex]3.0[\/latex]<\/td>\n<td>[latex]3.5[\/latex]<\/td>\n<td>[latex]4.0[\/latex]<\/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=\"q214538\">Show Solution<\/button> <\/p>\n<div id=\"q214538\" class=\"hidden-answer\" style=\"display: none\">\n<ol style=\"list-style-type: lower-alpha;\">\n<li>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.<\/li>\n<li>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 [latex]3.0[\/latex] could have a variety of percent grades ranging from [latex]78[\/latex] all the way to [latex]86[\/latex]. Thus, percent grade is not a function of grade point average.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox example\">Define the domain and range for the following set of ordered pairs, and determine whether the relation given is a function.<\/p>\n<p style=\"text-align: center;\">[latex]\\{(\u22123,\u22126),(\u22122,\u22121),(1,0),(1,5),(2,0)\\}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q507050\">Show Solution<\/button> <\/p>\n<div id=\"q507050\" class=\"hidden-answer\" style=\"display: none\"> We list all of the input values as the domain. &nbsp;The input values are represented first in the ordered pair as a matter of convention. <\/p>\n<p>Domain: {[latex]-3,-2,1,2[\/latex]} <\/p>\n<p>Note how we did not enter repeated values more than once; it is not necessary. <\/p>\n<p>The range is the list of outputs for the relation; they are entered second in the ordered pair. <\/p>\n<p>Range: {[latex]-6, -1, 0, 5[\/latex]} <\/p>\n<p>Organizing the ordered pairs in a table can help you tell whether this relation is a function. &nbsp;By definition, the inputs in a function have only one output.<\/p>\n<div style=\"text-align: center;\">\n<table style=\"width: 50%;\">\n<tbody>\n<tr>\n<th style=\"text-align: center;\" scope=\"row\"><i>x<\/i><\/th>\n<th style=\"text-align: center;\"><i>y<\/i><\/th>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" scope=\"row\">[latex]\u22123[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]\u22126[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" scope=\"row\">[latex]\u22122[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]\u22121[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" scope=\"row\">[latex]1[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]0[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" scope=\"row\">[latex]1[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]5[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" scope=\"row\">[latex]2[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]0[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<p>The relation is not a function because the input [latex]1[\/latex] has two outputs: [latex]0[\/latex] and [latex]5[\/latex].<\/p>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\">\n<iframe loading=\"lazy\" id=\"ohm13501\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=13501&theme=lumen&iframe_resize_id=ohm13501&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n","protected":false},"author":6,"menu_order":4,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Algebra and Trigonometry 2e\",\"author\":\"Jay Abramson\",\"organization\":\"OpenStax\",\"url\":\"https:\/\/openstax.org\/books\/algebra-and-trigonometry-2e\/pages\/3-1-functions-and-function-notation#Figure_01_01_013\",\"project\":\"3.1 Functions and Function Notation\",\"license\":\"cc-by\",\"license_terms\":\"Access for free at https:\/\/openstax.org\/books\/algebra-and-trigonometry-2e\/pages\/1-introduction-to-prerequisites\"}]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":185,"module-header":"","content_attributions":[{"type":"cc-attribution","description":"Algebra and Trigonometry 2e","author":"Jay Abramson","organization":"OpenStax","url":"https:\/\/openstax.org\/books\/algebra-and-trigonometry-2e\/pages\/3-1-functions-and-function-notation#Figure_01_01_013","project":"3.1 Functions and Function Notation","license":"cc-by","license_terms":"Access for free at https:\/\/openstax.org\/books\/algebra-and-trigonometry-2e\/pages\/1-introduction-to-prerequisites"}],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/pressbooks\/v2\/chapters\/189"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/wp\/v2\/users\/6"}],"version-history":[{"count":0,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/pressbooks\/v2\/chapters\/189\/revisions"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/pressbooks\/v2\/parts\/185"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/pressbooks\/v2\/chapters\/189\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/wp\/v2\/media?parent=189"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/pressbooks\/v2\/chapter-type?post=189"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/wp\/v2\/contributor?post=189"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/wp\/v2\/license?post=189"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}