{"id":5420,"date":"2021-01-27T17:47:43","date_gmt":"2021-01-27T17:47:43","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/?post_type=chapter&#038;p=5420"},"modified":"2025-11-30T03:38:42","modified_gmt":"2025-11-30T03:38:42","slug":"3-5-reading-and-analyzing-graphs","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/chapter\/3-5-reading-and-analyzing-graphs\/","title":{"raw":"3.5 Reading and Analyzing Graphs","rendered":"3.5 Reading and Analyzing Graphs"},"content":{"raw":"<h1 style=\"text-align: center;\">Reading and Analyzing Graphs<\/h1>\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\n<ul>\r\n \t<li>Analyze graphs by examining their features:\r\n<ul>\r\n \t<li>Graph Titles<\/li>\r\n \t<li>Axes Labels (and Units)<\/li>\r\n \t<li>Increasing\/Decreasing<\/li>\r\n \t<li>Maximums\/Minimums<\/li>\r\n \t<li>General Shape<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<\/div>\r\n<p style=\"font-size: 17px;\">Reading and analyzing graphs is important in almost every field of study. Graphs are everywhere: newspapers, magazines, on the Internet, research articles, business documents, etc. Graphs tell a story, in a visual way, about what is going on. They say a picture is worth a thousand words. Graphs can also communicate a thousand words of information in a compact format of a picture.<\/p>\r\nIn the below graph, we first notice the <strong>title<\/strong>, \"Quarterly Sales, Employee A\". The <strong>horizontal axes<\/strong> <strong>labels <\/strong>are Q1 2020, Q2 2020, etc. The <strong>vertical axes<\/strong> <strong>labels<\/strong> are dollars. From these three things, we can determine the story the graph is telling.\r\n\r\nThe graph is showing the quarterly sales for one particular employee (A). This employee's sales were a little less than $1,500 in the first quarter of 2020. Each quarter this employee's sales <strong>increase<\/strong> slightly through the fourth quarter of 2021 when their sales were a little less than $2,000.\r\n\r\nNote: When you read the graph left-to-right and the graph line goes up, we say the graph is <strong>increasing<\/strong>.\r\n\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/03175755\/Quarterly-Sales-Employee-A1.png\"><img class=\"wp-image-5494 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/03175755\/Quarterly-Sales-Employee-A1.png\" alt=\"\" width=\"756\" height=\"597\" \/><\/a>\r\n\r\nIn the following graph, we similarly notice the <strong>title<\/strong>, \"Quarterly Sales, Employee B\". The <strong>horizontal axes<\/strong> <strong>labels <\/strong>are Q1 2020, Q2 2020, etc. It appears Q1 is the first quarter, Q2 is the second quarter, and so on. The <strong>vertical axes<\/strong> <strong>labels<\/strong> are dollars.\r\n\r\nThe graph is showing the quarterly sales for a different\u00a0 employee (B). This employee's sales were approximately $1,500 in the first quarter of 2020. Each quarter this employee's sales <strong>decrease<\/strong> through the fourth quarter of 2021 when their sales were approximately $700.\r\n\r\nNote: When you read the graph left-to-right and the graph line goes down, we say the graph is<strong> dec<\/strong><strong>reasing<\/strong>.\r\n\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/03182541\/Quarterly-Sales-Employee-B-JPG..jpg\"><img class=\"wp-image-5500 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/03182541\/Quarterly-Sales-Employee-B-JPG..jpg\" alt=\"\" width=\"752\" height=\"582\" \/><\/a>\r\n\r\nIn the below graph, we first notice the <strong>title<\/strong>, \"Gallons of Fuel in a Boeing 747\". The <strong>horizontal axes<\/strong> <strong>label <\/strong>is Hours of Flying. The <strong>vertical axes<\/strong> is Fuel, in gallons. The horizontal axis ends at 11 hours. We can assume this graph is showing us the amount of fuel a Boeing 747 airplane burns in one 11 hour flight.\r\n\r\nAfter one hour of flight, the airplane has a little over 35,000 gallons of fuel. Because the line is going down as we read it left-to-right, we say the graph is <strong>decreasing<\/strong>. In addition, because the graph appears to be a perfectly straight line, this graph is called a <strong>linear graph<\/strong>.\r\n\r\nNote: The graph is not realistic to model a true flight of a 747 airplane. More fuel is needed to take off and reach flying altitude than to flying at a constant rate for the duration of the flight. What might a more realistic graph look like?\r\n\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/12\/28214803\/Gallons-of-Fuel-Fix.jpg\"><img class=\"wp-image-6689 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/12\/28214803\/Gallons-of-Fuel-Fix.jpg\" alt=\"\" width=\"603\" height=\"368\" \/><\/a>\r\n\r\nIn the next graph we notice the <strong>title<\/strong>, \"GPA vs. Hours Worked at Paid Job\". The <strong>horizontal axes<\/strong> <strong>labels <\/strong>are Hours Per Week Worked in Paid Job. The <strong>vertical axes<\/strong> is College GPA.\r\n\r\nThis graph appears to tell the story of students who attend college and also work in a paid job. Their corresponding GPA's (Grade Point Averages) are graphed. The GPA increases as students work from 10 to 25 hours, and decreases as the hours go from 25 to 40 hours. The <strong>maximum<\/strong> <strong>GPA<\/strong> can be thought of as the height (in the vertical direction) at the \"top of the peak.\" The graph suggests that GPA increases for students as they work in a paid job, up to about 25 hours. Then GPA goes down when students work more than 25 hours.\r\n\r\nThis shape of a graph is called a <strong>parabolic graph<\/strong>. Parabolic graphs come from <strong>quadratic functions<\/strong>. See below for more on parabolic graphs.\r\n\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/03185539\/quadratic1.jpg\"><img class=\"wp-image-5510 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/03185539\/quadratic1.jpg\" alt=\"\" width=\"720\" height=\"446\" \/><\/a>\r\n<table style=\"border-collapse: collapse; width: 100%; height: 28px;\" border=\"1\">\r\n<tbody>\r\n<tr style=\"height: 28px;\">\r\n<td style=\"width: 100%; height: 28px;\">\r\n<p style=\"font-size: 17px;\"><strong>Parabolic graphs<\/strong> can open \"upwards\" or \"downwards\". They can open wide or narrow. On parabolas that open downward, the highest vertical height of is called the <strong>maximum<\/strong>.\u00a0 On parabolas that open upward, the lowest vertical height of is called the <strong>minimum<\/strong>.<\/p>\r\n<p style=\"font-size: 17px;\">Examples of quadratic equations (those that create parabolas) include:<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/30195243\/quadratics1.jpg\"><img class=\"wp-image-6325 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/30195243\/quadratics1.jpg\" alt=\"\" width=\"420\" height=\"49\" \/><\/a><\/p>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"1\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%;\"><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/03194218\/Parabolas.jpg\"><img class=\"alignnone wp-image-5513\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/03194218\/Parabolas.jpg\" alt=\"\" width=\"712\" height=\"266\" \/><\/a><\/td>\r\n<td style=\"width: 50%;\"><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/03194250\/Parabolas-2.jpg\"><img class=\"alignnone wp-image-5514\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/03194250\/Parabolas-2.jpg\" alt=\"\" width=\"699\" height=\"319\" \/><\/a><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div class=\"textbox\"><strong>Exponential graphs<\/strong> also have a special look. If a quantity is growing exponentially, the graph will grow very slowly in the beginning and the increase at a seemingly drastic rate!<\/div>\r\nDuckweed is a plant that grows in ponds and covers the surface of the pond. This graph is modeling the surface area of the pond covered by duckweed over the period of a month.\r\n\r\nIn this graph the area, measured in square feet, starts out very small. It grows slowly until Day 22 or so. Then the surface starts increasing quickly. This type of growth is called<strong> exponential growth<\/strong>.\r\n\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/03235354\/Duckweed1.jpg\"><img class=\"wp-image-5518 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/03235354\/Duckweed1.jpg\" alt=\"\" width=\"786\" height=\"427\" \/><\/a>\r\n\r\nThe below graph shows the amount of remaining pie if half the remaining pie is eaten each day. We can see that there is one whole pie on Day 1. Then on Day 2, there is half of the pie left. Then on Day 3, half of a half, or one-fourth of the pie is remaining. Each day the amount of pie eaten gets smaller and smaller.\r\n\r\nThis type of graph is modeling <strong>exponential decay<\/strong>.\r\n\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/04015600\/Pie.jpg\"><img class=\"wp-image-5527 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/04015600\/Pie.jpg\" alt=\"\" width=\"768\" height=\"499\" \/><\/a>\r\n<p style=\"text-align: center;\"><strong><span style=\"color: #ff0000;\">This is the end of the section. Close this tab and proceed to the corresponding assignment.<\/span><\/strong><\/p>","rendered":"<h1 style=\"text-align: center;\">Reading and Analyzing Graphs<\/h1>\n<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<ul>\n<li>Analyze graphs by examining their features:\n<ul>\n<li>Graph Titles<\/li>\n<li>Axes Labels (and Units)<\/li>\n<li>Increasing\/Decreasing<\/li>\n<li>Maximums\/Minimums<\/li>\n<li>General Shape<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/div>\n<p style=\"font-size: 17px;\">Reading and analyzing graphs is important in almost every field of study. Graphs are everywhere: newspapers, magazines, on the Internet, research articles, business documents, etc. Graphs tell a story, in a visual way, about what is going on. They say a picture is worth a thousand words. Graphs can also communicate a thousand words of information in a compact format of a picture.<\/p>\n<p>In the below graph, we first notice the <strong>title<\/strong>, &#8220;Quarterly Sales, Employee A&#8221;. The <strong>horizontal axes<\/strong> <strong>labels <\/strong>are Q1 2020, Q2 2020, etc. The <strong>vertical axes<\/strong> <strong>labels<\/strong> are dollars. From these three things, we can determine the story the graph is telling.<\/p>\n<p>The graph is showing the quarterly sales for one particular employee (A). This employee&#8217;s sales were a little less than $1,500 in the first quarter of 2020. Each quarter this employee&#8217;s sales <strong>increase<\/strong> slightly through the fourth quarter of 2021 when their sales were a little less than $2,000.<\/p>\n<p>Note: When you read the graph left-to-right and the graph line goes up, we say the graph is <strong>increasing<\/strong>.<\/p>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/03175755\/Quarterly-Sales-Employee-A1.png\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-5494 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/03175755\/Quarterly-Sales-Employee-A1.png\" alt=\"\" width=\"756\" height=\"597\" \/><\/a><\/p>\n<p>In the following graph, we similarly notice the <strong>title<\/strong>, &#8220;Quarterly Sales, Employee B&#8221;. The <strong>horizontal axes<\/strong> <strong>labels <\/strong>are Q1 2020, Q2 2020, etc. It appears Q1 is the first quarter, Q2 is the second quarter, and so on. The <strong>vertical axes<\/strong> <strong>labels<\/strong> are dollars.<\/p>\n<p>The graph is showing the quarterly sales for a different\u00a0 employee (B). This employee&#8217;s sales were approximately $1,500 in the first quarter of 2020. Each quarter this employee&#8217;s sales <strong>decrease<\/strong> through the fourth quarter of 2021 when their sales were approximately $700.<\/p>\n<p>Note: When you read the graph left-to-right and the graph line goes down, we say the graph is<strong> dec<\/strong><strong>reasing<\/strong>.<\/p>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/03182541\/Quarterly-Sales-Employee-B-JPG..jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-5500 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/03182541\/Quarterly-Sales-Employee-B-JPG..jpg\" alt=\"\" width=\"752\" height=\"582\" \/><\/a><\/p>\n<p>In the below graph, we first notice the <strong>title<\/strong>, &#8220;Gallons of Fuel in a Boeing 747&#8221;. The <strong>horizontal axes<\/strong> <strong>label <\/strong>is Hours of Flying. The <strong>vertical axes<\/strong> is Fuel, in gallons. The horizontal axis ends at 11 hours. We can assume this graph is showing us the amount of fuel a Boeing 747 airplane burns in one 11 hour flight.<\/p>\n<p>After one hour of flight, the airplane has a little over 35,000 gallons of fuel. Because the line is going down as we read it left-to-right, we say the graph is <strong>decreasing<\/strong>. In addition, because the graph appears to be a perfectly straight line, this graph is called a <strong>linear graph<\/strong>.<\/p>\n<p>Note: The graph is not realistic to model a true flight of a 747 airplane. More fuel is needed to take off and reach flying altitude than to flying at a constant rate for the duration of the flight. What might a more realistic graph look like?<\/p>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/12\/28214803\/Gallons-of-Fuel-Fix.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-6689 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/12\/28214803\/Gallons-of-Fuel-Fix.jpg\" alt=\"\" width=\"603\" height=\"368\" \/><\/a><\/p>\n<p>In the next graph we notice the <strong>title<\/strong>, &#8220;GPA vs. Hours Worked at Paid Job&#8221;. The <strong>horizontal axes<\/strong> <strong>labels <\/strong>are Hours Per Week Worked in Paid Job. The <strong>vertical axes<\/strong> is College GPA.<\/p>\n<p>This graph appears to tell the story of students who attend college and also work in a paid job. Their corresponding GPA&#8217;s (Grade Point Averages) are graphed. The GPA increases as students work from 10 to 25 hours, and decreases as the hours go from 25 to 40 hours. The <strong>maximum<\/strong> <strong>GPA<\/strong> can be thought of as the height (in the vertical direction) at the &#8220;top of the peak.&#8221; The graph suggests that GPA increases for students as they work in a paid job, up to about 25 hours. Then GPA goes down when students work more than 25 hours.<\/p>\n<p>This shape of a graph is called a <strong>parabolic graph<\/strong>. Parabolic graphs come from <strong>quadratic functions<\/strong>. See below for more on parabolic graphs.<\/p>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/03185539\/quadratic1.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-5510 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/03185539\/quadratic1.jpg\" alt=\"\" width=\"720\" height=\"446\" \/><\/a><\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 28px;\">\n<tbody>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; height: 28px;\">\n<p style=\"font-size: 17px;\"><strong>Parabolic graphs<\/strong> can open &#8220;upwards&#8221; or &#8220;downwards&#8221;. They can open wide or narrow. On parabolas that open downward, the highest vertical height of is called the <strong>maximum<\/strong>.\u00a0 On parabolas that open upward, the lowest vertical height of is called the <strong>minimum<\/strong>.<\/p>\n<p style=\"font-size: 17px;\">Examples of quadratic equations (those that create parabolas) include:<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/30195243\/quadratics1.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-6325 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/30195243\/quadratics1.jpg\" alt=\"\" width=\"420\" height=\"49\" \/><\/a><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/03194218\/Parabolas.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-5513\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/03194218\/Parabolas.jpg\" alt=\"\" width=\"712\" height=\"266\" \/><\/a><\/td>\n<td style=\"width: 50%;\"><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/03194250\/Parabolas-2.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-5514\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/03194250\/Parabolas-2.jpg\" alt=\"\" width=\"699\" height=\"319\" \/><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"textbox\"><strong>Exponential graphs<\/strong> also have a special look. If a quantity is growing exponentially, the graph will grow very slowly in the beginning and the increase at a seemingly drastic rate!<\/div>\n<p>Duckweed is a plant that grows in ponds and covers the surface of the pond. This graph is modeling the surface area of the pond covered by duckweed over the period of a month.<\/p>\n<p>In this graph the area, measured in square feet, starts out very small. It grows slowly until Day 22 or so. Then the surface starts increasing quickly. This type of growth is called<strong> exponential growth<\/strong>.<\/p>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/03235354\/Duckweed1.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-5518 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/03235354\/Duckweed1.jpg\" alt=\"\" width=\"786\" height=\"427\" \/><\/a><\/p>\n<p>The below graph shows the amount of remaining pie if half the remaining pie is eaten each day. We can see that there is one whole pie on Day 1. Then on Day 2, there is half of the pie left. Then on Day 3, half of a half, or one-fourth of the pie is remaining. Each day the amount of pie eaten gets smaller and smaller.<\/p>\n<p>This type of graph is modeling <strong>exponential decay<\/strong>.<\/p>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/04015600\/Pie.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-5527 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/04015600\/Pie.jpg\" alt=\"\" width=\"768\" height=\"499\" \/><\/a><\/p>\n<p style=\"text-align: center;\"><strong><span style=\"color: #ff0000;\">This is the end of the section. Close this tab and proceed to the corresponding assignment.<\/span><\/strong><\/p>\n","protected":false},"author":359705,"menu_order":6,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-5420","chapter","type-chapter","status-publish","hentry"],"part":356,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/pressbooks\/v2\/chapters\/5420","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/wp\/v2\/users\/359705"}],"version-history":[{"count":55,"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/pressbooks\/v2\/chapters\/5420\/revisions"}],"predecessor-version":[{"id":5492,"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/pressbooks\/v2\/chapters\/5420\/revisions\/5492"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/pressbooks\/v2\/parts\/356"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/pressbooks\/v2\/chapters\/5420\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/wp\/v2\/media?parent=5420"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/pressbooks\/v2\/chapter-type?post=5420"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/wp\/v2\/contributor?post=5420"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/wp\/v2\/license?post=5420"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}