{"id":3766,"date":"2021-05-12T20:24:06","date_gmt":"2021-05-12T20:24:06","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/calculus1\/chapter\/1b\/"},"modified":"2021-05-12T20:24:06","modified_gmt":"2021-05-12T20:24:06","slug":"1b","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/calculus1\/chapter\/1b\/","title":{"raw":"Skills Review for Basic Classes of Functions","rendered":"Skills Review for Basic Classes of Functions"},"content":{"raw":"\n<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n \t<li>Evaluate a piecewise function<\/li>\n \t<li>Identify important features of the graphs of \"toolkit\" functions<\/li>\n<\/ul>\n<\/div>\nIn Section 1.2, you will graph piecewise-defined functions and basic toolkit \"parent\" functions using transformations. To prepare you for graphing piecewise-defined functions, how to evaluate them is reviewed here. An introduction to basic toolkit \"parent\" functions is also provided here in order to reacquaint you with these functions so you can graph them using transformations.\n<h2>Evaluate Piecewise-defined Functions<\/h2>\nSometimes, we come across a function that requires more than one formula in order to obtain the given output. A <strong>piecewise-defined function<\/strong> is a function in which more than one formula is used to define the output over different pieces of the domain.\n\nWe use piecewise functions to describe situations in which a rule or relationship changes as the input value crosses certain \"boundaries.\" For example, we often encounter situations in business for which the cost per piece of a certain item is discounted once the number ordered exceeds a certain value. Tax brackets are another real-world example of piecewise functions. For example, consider a simple tax system in which incomes up to [latex]$10,000[\/latex] are taxed at [latex]10%[\/latex], and any additional income is taxed at [latex]20\\%[\/latex]. The tax on a total income, [latex] S[\/latex] , would be&nbsp;[latex]0.1S[\/latex] if [latex]{S}\\le$10,000[\/latex] &nbsp;and [latex]1000 + 0.2 (S - $10,000)[\/latex] ,&nbsp;if [latex] S&gt; $10,000[\/latex] .\n<div class=\"textbox\">\n<h3>A General Note: Piecewise-defined Functions<\/h3>\nA piecewise-defined function is a function in which more than one formula is used to define the output. Each formula has its own domain, and the domain of the function is the union of all these smaller domains. We notate this idea like this:\n<p style=\"text-align: center;\">[latex] f\\left(x\\right)=\\begin{cases}\\text{formula 1 if x is in domain 1}\\\\ \\text{formula 2 if x is in domain 2}\\\\ \\text{formula 3 if x is in domain 3}\\end{cases} [\/latex]<\/p>\n\n<\/div>\n<div class=\"textbox\">\n<h3>How To:&nbsp;Given a piecewise-Defined function, Evaluate it at a particular domain value<strong>\n<\/strong><\/h3>\n<ol>\n \t<li>Identify which piece of the function is defined at the given domain value.<\/li>\n \t<li>Plug the domain value into the piece where it is defined.<\/li>\n \t<li>Evaluate.<\/li>\n<\/ol>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example: Evaluating a Piecewise-Defined Function<\/h3>\nA cell phone company uses the function below to determine the cost, [latex]C[\/latex], in dollars for [latex]g[\/latex] gigabytes of data transfer.\n<p style=\"text-align: center;\">[latex]C\\left(g\\right)=\\begin{cases}\\begin{align}{25} \\hspace{2mm}&amp;\\text{ if }\\hspace{2mm}{ 0 }&lt;{ g }&lt;{ 2 }\\\\ { 25+10 }\\left(g - 2\\right) \\hspace{2mm}&amp;\\text{ if }\\hspace{2mm}{ g}\\ge{ 2 }\\end{align}\\end{cases}[\/latex]<\/p>\nFind the cost of using 1.5 gigabytes of data and the cost of using 4 gigabytes of data.\n\n[reveal-answer q=\"220698\"]Show Solution[\/reveal-answer]\n[hidden-answer a=\"220698\"]\n\nTo find the cost of using 1.5 gigabytes of data, [latex]C(1.5)[\/latex], we first look to see which part of the domain our input falls in. Because 1.5 is less than 2, we use the first formula.\n<p style=\"text-align: center;\">[latex]C(1.5) = $25[\/latex]<\/p>\nTo find the cost of using 4 gigabytes of data, [latex]C(4)[\/latex], we see that our input of 4 is greater than 2, so we use the second formula.\n<p style=\"text-align: center;\">[latex]C(4)=25 + 10( 4-2) =$45[\/latex]<\/p>\n[\/hidden-answer]\n\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n[ohm_question]218999[\/ohm_question]\n\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n[ohm_question]219000[\/ohm_question]\n\n<\/div>\n<h2>Identify Basic Toolkit \"Parent\" Functions<\/h2>\nBelow you will see information about basic toolkit \"parent\" functions, some of which will be useful in Section 1.2. It will be very helpful if we can recognize these toolkit functions and their features quickly by name, formula, graph, and basic table properties. The graphs and sample table values are included with each function shown below.\n<table>\n<thead>\n<tr>\n<th colspan=\"3\">Toolkit Functions<\/th>\n<\/tr>\n<tr>\n<th>Name<\/th>\n<th>Function<\/th>\n<th>Graph<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Constant<\/td>\n<td>[latex]f\\left(x\\right)=c[\/latex], where [latex]c[\/latex] is a constant<\/td>\n<td><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2016\/10\/18191028\/CNX_Precalc_Figure_01_01_018n.jpg\" alt=\"Graph of a constant function.\" width=\"517\" height=\"319\"><\/td>\n<\/tr>\n<tr>\n<td>Identity<\/td>\n<td>[latex]f\\left(x\\right)=x[\/latex]<\/td>\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2016\/10\/18191030\/CNX_Precalc_Figure_01_01_019n.jpg\" alt=\"Graph of a straight line.\"><\/td>\n<\/tr>\n<tr>\n<td>Absolute value<\/td>\n<td>[latex]f\\left(x\\right)=|x|[\/latex]<\/td>\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2016\/10\/18191034\/CNX_Precalc_Figure_01_01_020n.jpg\" alt=\"Graph of absolute function.\"><\/td>\n<\/tr>\n<tr>\n<td>Quadratic<\/td>\n<td>[latex]f\\left(x\\right)={x}^{2}[\/latex]<\/td>\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2016\/10\/18191037\/CNX_Precalc_Figure_01_01_021n.jpg\" alt=\"Graph of a parabola.\"><\/td>\n<\/tr>\n<tr>\n<td>Cubic<\/td>\n<td>[latex]f\\left(x\\right)={x}^{3}[\/latex]<\/td>\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2016\/10\/18191039\/CNX_Precalc_Figure_01_01_022n.jpg\" alt=\"Graph of f(x) = x^3.\"><\/td>\n<\/tr>\n<tr>\n<td>Reciprocal\/ Rational<\/td>\n<td>[latex]f\\left(x\\right)=\\frac{1}{x}[\/latex]<\/td>\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2016\/10\/18191042\/CNX_Precalc_Figure_01_01_023n.jpg\" alt=\"Graph of f(x)=1\/x.\"><\/td>\n<\/tr>\n<tr>\n<td>Reciprocal \/ Rational squared<\/td>\n<td>[latex]f\\left(x\\right)=\\frac{1}{{x}^{2}}[\/latex]<\/td>\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2016\/10\/18191044\/CNX_Precalc_Figure_01_01_024n.jpg\" alt=\"Graph of f(x)=1\/x^2.\"><\/td>\n<\/tr>\n<tr>\n<td>Square root<\/td>\n<td>[latex]f\\left(x\\right)=\\sqrt{x}[\/latex]<\/td>\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2016\/10\/18191047\/CNX_Precalc_Figure_01_01_025n.jpg\" alt=\"Graph of f(x)=sqrt(x).\"><\/td>\n<\/tr>\n<tr>\n<td>Cube root<\/td>\n<td>[latex]f\\left(x\\right)=\\sqrt[3]{x}[\/latex]<\/td>\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2016\/10\/18191050\/CNX_Precalc_Figure_01_01_026n.jpg\" alt=\"Graph of f(x)=x^(1\/3).\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n[ohm_question]111722[\/ohm_question]\n\n<\/div>\n","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Evaluate a piecewise function<\/li>\n<li>Identify important features of the graphs of &#8220;toolkit&#8221; functions<\/li>\n<\/ul>\n<\/div>\n<p>In Section 1.2, you will graph piecewise-defined functions and basic toolkit &#8220;parent&#8221; functions using transformations. To prepare you for graphing piecewise-defined functions, how to evaluate them is reviewed here. An introduction to basic toolkit &#8220;parent&#8221; functions is also provided here in order to reacquaint you with these functions so you can graph them using transformations.<\/p>\n<h2>Evaluate Piecewise-defined Functions<\/h2>\n<p>Sometimes, we come across a function that requires more than one formula in order to obtain the given output. A <strong>piecewise-defined function<\/strong> is a function in which more than one formula is used to define the output over different pieces of the domain.<\/p>\n<p>We use piecewise functions to describe situations in which a rule or relationship changes as the input value crosses certain &#8220;boundaries.&#8221; For example, we often encounter situations in business for which the cost per piece of a certain item is discounted once the number ordered exceeds a certain value. Tax brackets are another real-world example of piecewise functions. For example, consider a simple tax system in which incomes up to [latex]$10,000[\/latex] are taxed at [latex]10%[\/latex], and any additional income is taxed at [latex]20\\%[\/latex]. The tax on a total income, [latex]S[\/latex] , would be&nbsp;[latex]0.1S[\/latex] if [latex]{S}\\le$10,000[\/latex] &nbsp;and [latex]1000 + 0.2 (S - $10,000)[\/latex] ,&nbsp;if [latex]S> $10,000[\/latex] .<\/p>\n<div class=\"textbox\">\n<h3>A General Note: Piecewise-defined Functions<\/h3>\n<p>A piecewise-defined function is a function in which more than one formula is used to define the output. Each formula has its own domain, and the domain of the function is the union of all these smaller domains. We notate this idea like this:<\/p>\n<p style=\"text-align: center;\">[latex]f\\left(x\\right)=\\begin{cases}\\text{formula 1 if x is in domain 1}\\\\ \\text{formula 2 if x is in domain 2}\\\\ \\text{formula 3 if x is in domain 3}\\end{cases}[\/latex]<\/p>\n<\/div>\n<div class=\"textbox\">\n<h3>How To:&nbsp;Given a piecewise-Defined function, Evaluate it at a particular domain value<strong><br \/>\n<\/strong><\/h3>\n<ol>\n<li>Identify which piece of the function is defined at the given domain value.<\/li>\n<li>Plug the domain value into the piece where it is defined.<\/li>\n<li>Evaluate.<\/li>\n<\/ol>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example: Evaluating a Piecewise-Defined Function<\/h3>\n<p>A cell phone company uses the function below to determine the cost, [latex]C[\/latex], in dollars for [latex]g[\/latex] gigabytes of data transfer.<\/p>\n<p style=\"text-align: center;\">[latex]C\\left(g\\right)=\\begin{cases}\\begin{align}{25} \\hspace{2mm}&\\text{ if }\\hspace{2mm}{ 0 }<{ g }<{ 2 }\\\\ { 25+10 }\\left(g - 2\\right) \\hspace{2mm}&\\text{ if }\\hspace{2mm}{ g}\\ge{ 2 }\\end{align}\\end{cases}[\/latex]<\/p>\n<p>Find the cost of using 1.5 gigabytes of data and the cost of using 4 gigabytes of data.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q220698\">Show Solution<\/span><\/p>\n<div id=\"q220698\" class=\"hidden-answer\" style=\"display: none\">\n<p>To find the cost of using 1.5 gigabytes of data, [latex]C(1.5)[\/latex], we first look to see which part of the domain our input falls in. Because 1.5 is less than 2, we use the first formula.<\/p>\n<p style=\"text-align: center;\">[latex]C(1.5) = $25[\/latex]<\/p>\n<p>To find the cost of using 4 gigabytes of data, [latex]C(4)[\/latex], we see that our input of 4 is greater than 2, so we use the second formula.<\/p>\n<p style=\"text-align: center;\">[latex]C(4)=25 + 10( 4-2) =$45[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm218999\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=218999&theme=oea&iframe_resize_id=ohm218999&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm219000\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=219000&theme=oea&iframe_resize_id=ohm219000&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<h2>Identify Basic Toolkit &#8220;Parent&#8221; Functions<\/h2>\n<p>Below you will see information about basic toolkit &#8220;parent&#8221; functions, some of which will be useful in Section 1.2. It will be very helpful if we can recognize these toolkit functions and their features quickly by name, formula, graph, and basic table properties. The graphs and sample table values are included with each function shown below.<\/p>\n<table>\n<thead>\n<tr>\n<th colspan=\"3\">Toolkit Functions<\/th>\n<\/tr>\n<tr>\n<th>Name<\/th>\n<th>Function<\/th>\n<th>Graph<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Constant<\/td>\n<td>[latex]f\\left(x\\right)=c[\/latex], where [latex]c[\/latex] is a constant<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2016\/10\/18191028\/CNX_Precalc_Figure_01_01_018n.jpg\" alt=\"Graph of a constant function.\" width=\"517\" height=\"319\" \/><\/td>\n<\/tr>\n<tr>\n<td>Identity<\/td>\n<td>[latex]f\\left(x\\right)=x[\/latex]<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2016\/10\/18191030\/CNX_Precalc_Figure_01_01_019n.jpg\" alt=\"Graph of a straight line.\" \/><\/td>\n<\/tr>\n<tr>\n<td>Absolute value<\/td>\n<td>[latex]f\\left(x\\right)=|x|[\/latex]<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2016\/10\/18191034\/CNX_Precalc_Figure_01_01_020n.jpg\" alt=\"Graph of absolute function.\" \/><\/td>\n<\/tr>\n<tr>\n<td>Quadratic<\/td>\n<td>[latex]f\\left(x\\right)={x}^{2}[\/latex]<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2016\/10\/18191037\/CNX_Precalc_Figure_01_01_021n.jpg\" alt=\"Graph of a parabola.\" \/><\/td>\n<\/tr>\n<tr>\n<td>Cubic<\/td>\n<td>[latex]f\\left(x\\right)={x}^{3}[\/latex]<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2016\/10\/18191039\/CNX_Precalc_Figure_01_01_022n.jpg\" alt=\"Graph of f(x) = x^3.\" \/><\/td>\n<\/tr>\n<tr>\n<td>Reciprocal\/ Rational<\/td>\n<td>[latex]f\\left(x\\right)=\\frac{1}{x}[\/latex]<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2016\/10\/18191042\/CNX_Precalc_Figure_01_01_023n.jpg\" alt=\"Graph of f(x)=1\/x.\" \/><\/td>\n<\/tr>\n<tr>\n<td>Reciprocal \/ Rational squared<\/td>\n<td>[latex]f\\left(x\\right)=\\frac{1}{{x}^{2}}[\/latex]<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2016\/10\/18191044\/CNX_Precalc_Figure_01_01_024n.jpg\" alt=\"Graph of f(x)=1\/x^2.\" \/><\/td>\n<\/tr>\n<tr>\n<td>Square root<\/td>\n<td>[latex]f\\left(x\\right)=\\sqrt{x}[\/latex]<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2016\/10\/18191047\/CNX_Precalc_Figure_01_01_025n.jpg\" alt=\"Graph of f(x)=sqrt(x).\" \/><\/td>\n<\/tr>\n<tr>\n<td>Cube root<\/td>\n<td>[latex]f\\left(x\\right)=\\sqrt[3]{x}[\/latex]<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2016\/10\/18191050\/CNX_Precalc_Figure_01_01_026n.jpg\" alt=\"Graph of f(x)=x^(1\/3).\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm111722\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=111722&theme=oea&iframe_resize_id=ohm111722&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\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-3766\">\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>Modification and Revision. <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>College Algebra Corequisite. <strong>Provided by<\/strong>: Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/courses.lumenlearning.com\/waymakercollegealgebracorequisite\/\">https:\/\/courses.lumenlearning.com\/waymakercollegealgebracorequisite\/<\/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>Precalculus. <strong>Provided by<\/strong>: Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/courses.lumenlearning.com\/precalculus\/\">https:\/\/courses.lumenlearning.com\/precalculus\/<\/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":17533,"menu_order":2,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"College Algebra Corequisite\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"https:\/\/courses.lumenlearning.com\/waymakercollegealgebracorequisite\/\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Precalculus\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"https:\/\/courses.lumenlearning.com\/precalculus\/\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Modification and Revision\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-3766","chapter","type-chapter","status-publish","hentry"],"part":3764,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3766","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":0,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3766\/revisions"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/parts\/3764"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3766\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/media?parent=3766"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapter-type?post=3766"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/contributor?post=3766"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/license?post=3766"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}