{"id":105,"date":"2025-04-09T17:09:08","date_gmt":"2025-04-09T17:09:08","guid":{"rendered":"https:\/\/pressbooks.ccconline.org\/ccacollegealgebra\/?post_type=part&#038;p=105"},"modified":"2025-08-13T14:00:56","modified_gmt":"2025-08-13T14:00:56","slug":"chapter-3-functions","status":"publish","type":"part","link":"https:\/\/pressbooks.ccconline.org\/ccacollegealgebra\/part\/chapter-3-functions\/","title":{"raw":"Chapter 3: Functions","rendered":"Chapter 3: Functions"},"content":{"raw":"<div class=\"intro-text\">\r\n<div>\r\n<div>\r\n\r\n[caption id=\"attachment_444\" align=\"aligncenter\" width=\"415\"]<img class=\"wp-image-444\" src=\"https:\/\/pressbooks.ccconline.org\/ccacollegealgebra\/wp-content\/uploads\/sites\/234\/2025\/04\/\u0421oronavirus._SARS-CoV-2-300x300.jpg\" alt=\"\" width=\"415\" height=\"415\" \/> \"Coronavirus. SARS-CoV-2\" by Alexey Solodovnikiv is licensed under CC BY-SA 4.0.[\/caption]\r\n\r\n[caption id=\"attachment_445\" align=\"aligncenter\" width=\"525\"]<img class=\"wp-image-445\" src=\"https:\/\/pressbooks.ccconline.org\/ccacollegealgebra\/wp-content\/uploads\/sites\/234\/2025\/04\/Covid-19_new_cases_in_top_5_countries_and_the_world-300x207.png\" alt=\"\" width=\"525\" height=\"362\" \/> \"Covid-19 new cases in top 5 countries and the world\" by Chris55 is licensed under CC BY-SA 4.0.[\/caption]\r\n\r\n<div class=\"os-chapter-outline\">\r\n<h2 class=\"os-title\">Chapter Outline<\/h2>\r\n<div class=\"os-chapter-objective\"><a class=\"os-chapter-objective\" href=\"https:\/\/pressbooks.ccconline.org\/ccacollegealgebra\/chapter\/3-1-functions-and-function-notation\/\" data-page-slug=\"3-1-functions-and-function-notation\" data-page-uuid=\"55f2e8ec-a982-4586-9d48-a2f43d7b4107\" data-page-fragment=\"\"> <span class=\"os-number\">3.1<\/span> <span class=\"os-text\" data-type=\"\">Functions and Function Notation<\/span> <\/a><\/div>\r\n<div class=\"os-chapter-objective\"><a class=\"os-chapter-objective\" href=\"https:\/\/pressbooks.ccconline.org\/ccacollegealgebra\/chapter\/3-2-domain-and-range\/\" data-page-slug=\"3-2-domain-and-range\" data-page-uuid=\"562c3737-a93d-458c-98c0-a04f442f13bd\" data-page-fragment=\"\"> <span class=\"os-number\">3.2<\/span> <span class=\"os-text\" data-type=\"\">Domain and Range<\/span> <\/a><\/div>\r\n<div class=\"os-chapter-objective\"><a class=\"os-chapter-objective\" href=\"https:\/\/pressbooks.ccconline.org\/ccacollegealgebra\/chapter\/3-3-rates-of-change-and-behavior-of-graphs\/\" data-page-slug=\"3-3-rates-of-change-and-behavior-of-graphs\" data-page-uuid=\"f37919d7-b496-4e36-8196-431ae4733a64\" data-page-fragment=\"\"> <span class=\"os-number\">3.3<\/span> <span class=\"os-text\" data-type=\"\">Rates of Change and Behavior of Graphs<\/span> <\/a><\/div>\r\n<div class=\"os-chapter-objective\"><a class=\"os-chapter-objective\" href=\"https:\/\/pressbooks.ccconline.org\/ccacollegealgebra\/chapter\/3-4-composition-of-functions\/\" data-page-slug=\"3-4-composition-of-functions\" data-page-uuid=\"8a4fc477-43da-4fc4-9ff0-19a7fae5a19d\" data-page-fragment=\"\"> <span class=\"os-number\">3.4<\/span> <span class=\"os-text\" data-type=\"\">Composition of Functions<\/span> <\/a><\/div>\r\n<div class=\"os-chapter-objective\"><a class=\"os-chapter-objective\" href=\"https:\/\/pressbooks.ccconline.org\/ccacollegealgebra\/chapter\/3-5-transformation-of-functions\/\" data-page-slug=\"3-5-transformation-of-functions\" data-page-uuid=\"5f6ff02a-1000-410d-b034-af26fbd86d0b\" data-page-fragment=\"\"> <span class=\"os-number\">3.5<\/span> <span class=\"os-text\" data-type=\"\">Transformation of Functions<\/span> <\/a><\/div>\r\n<div class=\"os-chapter-objective\"><a class=\"os-chapter-objective\" href=\"https:\/\/pressbooks.ccconline.org\/ccacollegealgebra\/chapter\/3-6-absolute-value-functions\/\" data-page-slug=\"3-6-absolute-value-functions\" data-page-uuid=\"2e387575-c04f-40e1-8895-195affae8fdb\" data-page-fragment=\"\"> <span class=\"os-number\">3.6<\/span> <span class=\"os-text\" data-type=\"\">Absolute Value Functions<\/span> <\/a><\/div>\r\n<div class=\"os-chapter-objective\"><a class=\"os-chapter-objective\" href=\"https:\/\/pressbooks.ccconline.org\/ccacollegealgebra\/chapter\/3-7-inverse-functions\/\" data-page-slug=\"3-7-inverse-functions\" data-page-uuid=\"f592aad0-19d8-42d6-94b9-086bdd84c2b5\" data-page-fragment=\"\"> <span class=\"os-number\">3.7<\/span> <span class=\"os-text\" data-type=\"\">Inverse Functions<\/span> <\/a><\/div>\r\n<\/div>\r\nThe COVID-19 pandemic caused by severe acute respiratory syndrome coronavirus 2 (<a href=\"https:\/\/en.wikipedia.org\/wiki\/SARS-CoV-2\" target=\"_blank\" rel=\"noopener\">SARS-CoV-2<\/a>), began with an <a href=\"https:\/\/en.wikipedia.org\/wiki\/Disease_outbreak\" target=\"_blank\" rel=\"noopener\">outbreak<\/a> of <a href=\"https:\/\/en.wikipedia.org\/wiki\/COVID-19\" target=\"_blank\" rel=\"noopener\">COVID-19<\/a> in <a href=\"https:\/\/en.wikipedia.org\/wiki\/Wuhan\" target=\"_blank\" rel=\"noopener\">Wuhan<\/a>, China, in December 2019. The graph above tracks the number of cases in 2022 for different countries and the whole world.\r\n\r\n<\/div>\r\n<div>\r\n\r\nNotice, as we consider this example, that there is a definite relationship between week and the number of cases. For any week we choose, we can determine the corresponding number of cases. In this chapter, we will explore these kinds of relationships and their properties.\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>","rendered":"<div class=\"intro-text\">\n<div>\n<div>\n<figure id=\"attachment_444\" aria-describedby=\"caption-attachment-444\" style=\"width: 415px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-444\" src=\"https:\/\/pressbooks.ccconline.org\/ccacollegealgebra\/wp-content\/uploads\/sites\/234\/2025\/04\/\u0421oronavirus._SARS-CoV-2-300x300.jpg\" alt=\"\" width=\"415\" height=\"415\" srcset=\"https:\/\/pressbooks.ccconline.org\/ccacollegealgebra\/wp-content\/uploads\/sites\/234\/2025\/04\/\u0421oronavirus._SARS-CoV-2-300x300.jpg 300w, https:\/\/pressbooks.ccconline.org\/ccacollegealgebra\/wp-content\/uploads\/sites\/234\/2025\/04\/\u0421oronavirus._SARS-CoV-2-150x150.jpg 150w, https:\/\/pressbooks.ccconline.org\/ccacollegealgebra\/wp-content\/uploads\/sites\/234\/2025\/04\/\u0421oronavirus._SARS-CoV-2-768x768.jpg 768w, https:\/\/pressbooks.ccconline.org\/ccacollegealgebra\/wp-content\/uploads\/sites\/234\/2025\/04\/\u0421oronavirus._SARS-CoV-2-65x65.jpg 65w, https:\/\/pressbooks.ccconline.org\/ccacollegealgebra\/wp-content\/uploads\/sites\/234\/2025\/04\/\u0421oronavirus._SARS-CoV-2-225x225.jpg 225w, https:\/\/pressbooks.ccconline.org\/ccacollegealgebra\/wp-content\/uploads\/sites\/234\/2025\/04\/\u0421oronavirus._SARS-CoV-2-350x350.jpg 350w, https:\/\/pressbooks.ccconline.org\/ccacollegealgebra\/wp-content\/uploads\/sites\/234\/2025\/04\/\u0421oronavirus._SARS-CoV-2.jpg 960w\" sizes=\"auto, (max-width: 415px) 100vw, 415px\" \/><figcaption id=\"caption-attachment-444\" class=\"wp-caption-text\">&#8220;Coronavirus. SARS-CoV-2&#8221; by Alexey Solodovnikiv is licensed under CC BY-SA 4.0.<\/figcaption><\/figure>\n<figure id=\"attachment_445\" aria-describedby=\"caption-attachment-445\" style=\"width: 525px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-445\" src=\"https:\/\/pressbooks.ccconline.org\/ccacollegealgebra\/wp-content\/uploads\/sites\/234\/2025\/04\/Covid-19_new_cases_in_top_5_countries_and_the_world-300x207.png\" alt=\"\" width=\"525\" height=\"362\" srcset=\"https:\/\/pressbooks.ccconline.org\/ccacollegealgebra\/wp-content\/uploads\/sites\/234\/2025\/04\/Covid-19_new_cases_in_top_5_countries_and_the_world-300x207.png 300w, https:\/\/pressbooks.ccconline.org\/ccacollegealgebra\/wp-content\/uploads\/sites\/234\/2025\/04\/Covid-19_new_cases_in_top_5_countries_and_the_world-768x531.png 768w, https:\/\/pressbooks.ccconline.org\/ccacollegealgebra\/wp-content\/uploads\/sites\/234\/2025\/04\/Covid-19_new_cases_in_top_5_countries_and_the_world-65x45.png 65w, https:\/\/pressbooks.ccconline.org\/ccacollegealgebra\/wp-content\/uploads\/sites\/234\/2025\/04\/Covid-19_new_cases_in_top_5_countries_and_the_world-225x156.png 225w, https:\/\/pressbooks.ccconline.org\/ccacollegealgebra\/wp-content\/uploads\/sites\/234\/2025\/04\/Covid-19_new_cases_in_top_5_countries_and_the_world-350x242.png 350w, https:\/\/pressbooks.ccconline.org\/ccacollegealgebra\/wp-content\/uploads\/sites\/234\/2025\/04\/Covid-19_new_cases_in_top_5_countries_and_the_world.png 800w\" sizes=\"auto, (max-width: 525px) 100vw, 525px\" \/><figcaption id=\"caption-attachment-445\" class=\"wp-caption-text\">&#8220;Covid-19 new cases in top 5 countries and the world&#8221; by Chris55 is licensed under CC BY-SA 4.0.<\/figcaption><\/figure>\n<div class=\"os-chapter-outline\">\n<h2 class=\"os-title\">Chapter Outline<\/h2>\n<div class=\"os-chapter-objective\"><a class=\"os-chapter-objective\" href=\"https:\/\/pressbooks.ccconline.org\/ccacollegealgebra\/chapter\/3-1-functions-and-function-notation\/\" data-page-slug=\"3-1-functions-and-function-notation\" data-page-uuid=\"55f2e8ec-a982-4586-9d48-a2f43d7b4107\" data-page-fragment=\"\"> <span class=\"os-number\">3.1<\/span> <span class=\"os-text\" data-type=\"\">Functions and Function Notation<\/span> <\/a><\/div>\n<div class=\"os-chapter-objective\"><a class=\"os-chapter-objective\" href=\"https:\/\/pressbooks.ccconline.org\/ccacollegealgebra\/chapter\/3-2-domain-and-range\/\" data-page-slug=\"3-2-domain-and-range\" data-page-uuid=\"562c3737-a93d-458c-98c0-a04f442f13bd\" data-page-fragment=\"\"> <span class=\"os-number\">3.2<\/span> <span class=\"os-text\" data-type=\"\">Domain and Range<\/span> <\/a><\/div>\n<div class=\"os-chapter-objective\"><a class=\"os-chapter-objective\" href=\"https:\/\/pressbooks.ccconline.org\/ccacollegealgebra\/chapter\/3-3-rates-of-change-and-behavior-of-graphs\/\" data-page-slug=\"3-3-rates-of-change-and-behavior-of-graphs\" data-page-uuid=\"f37919d7-b496-4e36-8196-431ae4733a64\" data-page-fragment=\"\"> <span class=\"os-number\">3.3<\/span> <span class=\"os-text\" data-type=\"\">Rates of Change and Behavior of Graphs<\/span> <\/a><\/div>\n<div class=\"os-chapter-objective\"><a class=\"os-chapter-objective\" href=\"https:\/\/pressbooks.ccconline.org\/ccacollegealgebra\/chapter\/3-4-composition-of-functions\/\" data-page-slug=\"3-4-composition-of-functions\" data-page-uuid=\"8a4fc477-43da-4fc4-9ff0-19a7fae5a19d\" data-page-fragment=\"\"> <span class=\"os-number\">3.4<\/span> <span class=\"os-text\" data-type=\"\">Composition of Functions<\/span> <\/a><\/div>\n<div class=\"os-chapter-objective\"><a class=\"os-chapter-objective\" href=\"https:\/\/pressbooks.ccconline.org\/ccacollegealgebra\/chapter\/3-5-transformation-of-functions\/\" data-page-slug=\"3-5-transformation-of-functions\" data-page-uuid=\"5f6ff02a-1000-410d-b034-af26fbd86d0b\" data-page-fragment=\"\"> <span class=\"os-number\">3.5<\/span> <span class=\"os-text\" data-type=\"\">Transformation of Functions<\/span> <\/a><\/div>\n<div class=\"os-chapter-objective\"><a class=\"os-chapter-objective\" href=\"https:\/\/pressbooks.ccconline.org\/ccacollegealgebra\/chapter\/3-6-absolute-value-functions\/\" data-page-slug=\"3-6-absolute-value-functions\" data-page-uuid=\"2e387575-c04f-40e1-8895-195affae8fdb\" data-page-fragment=\"\"> <span class=\"os-number\">3.6<\/span> <span class=\"os-text\" data-type=\"\">Absolute Value Functions<\/span> <\/a><\/div>\n<div class=\"os-chapter-objective\"><a class=\"os-chapter-objective\" href=\"https:\/\/pressbooks.ccconline.org\/ccacollegealgebra\/chapter\/3-7-inverse-functions\/\" data-page-slug=\"3-7-inverse-functions\" data-page-uuid=\"f592aad0-19d8-42d6-94b9-086bdd84c2b5\" data-page-fragment=\"\"> <span class=\"os-number\">3.7<\/span> <span class=\"os-text\" data-type=\"\">Inverse Functions<\/span> <\/a><\/div>\n<\/div>\n<p>The COVID-19 pandemic caused by severe acute respiratory syndrome coronavirus 2 (<a href=\"https:\/\/en.wikipedia.org\/wiki\/SARS-CoV-2\" target=\"_blank\" rel=\"noopener\">SARS-CoV-2<\/a>), began with an <a href=\"https:\/\/en.wikipedia.org\/wiki\/Disease_outbreak\" target=\"_blank\" rel=\"noopener\">outbreak<\/a> of <a href=\"https:\/\/en.wikipedia.org\/wiki\/COVID-19\" target=\"_blank\" rel=\"noopener\">COVID-19<\/a> in <a href=\"https:\/\/en.wikipedia.org\/wiki\/Wuhan\" target=\"_blank\" rel=\"noopener\">Wuhan<\/a>, China, in December 2019. The graph above tracks the number of cases in 2022 for different countries and the whole world.<\/p>\n<\/div>\n<div>\n<p>Notice, as we consider this example, that there is a definite relationship between week and the number of cases. For any week we choose, we can determine the corresponding number of cases. In this chapter, we will explore these kinds of relationships and their properties.<\/p>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"parent":0,"menu_order":4,"template":"","meta":{"pb_part_invisible":false,"pb_part_invisible_string":""},"contributor":[],"license":[],"class_list":["post-105","part","type-part","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pressbooks.ccconline.org\/ccacollegealgebra\/wp-json\/pressbooks\/v2\/parts\/105","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.ccconline.org\/ccacollegealgebra\/wp-json\/pressbooks\/v2\/parts"}],"about":[{"href":"https:\/\/pressbooks.ccconline.org\/ccacollegealgebra\/wp-json\/wp\/v2\/types\/part"}],"version-history":[{"count":6,"href":"https:\/\/pressbooks.ccconline.org\/ccacollegealgebra\/wp-json\/pressbooks\/v2\/parts\/105\/revisions"}],"predecessor-version":[{"id":1311,"href":"https:\/\/pressbooks.ccconline.org\/ccacollegealgebra\/wp-json\/pressbooks\/v2\/parts\/105\/revisions\/1311"}],"wp:attachment":[{"href":"https:\/\/pressbooks.ccconline.org\/ccacollegealgebra\/wp-json\/wp\/v2\/media?parent=105"}],"wp:term":[{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.ccconline.org\/ccacollegealgebra\/wp-json\/wp\/v2\/contributor?post=105"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.ccconline.org\/ccacollegealgebra\/wp-json\/wp\/v2\/license?post=105"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}