{"id":976,"date":"2016-10-20T23:26:03","date_gmt":"2016-10-20T23:26:03","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/waymakercollegealgebra\/?post_type=chapter&#038;p=976"},"modified":"2017-08-15T21:03:14","modified_gmt":"2017-08-15T21:03:14","slug":"introduction-domain-and-range-of-functions","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/chapter\/introduction-domain-and-range-of-functions\/","title":{"raw":"Introduction to Domain and Range of Functions","rendered":"Introduction to Domain and Range of Functions"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\">\r\n<h3>LEARNING OBJECTIVES<\/h3>\r\nBy the end of this lesson, you will be able to:\r\n<ul>\r\n \t<li>Find the domain of a function defined by an equation<\/li>\r\n \t<li>Write Domain and Range Using Standard Notations<\/li>\r\n \t<li>Find Domain and Range from a Graph<\/li>\r\n \t<li>Define Domain and Range of Toolkit Functions<\/li>\r\n \t<li>Graph Piecewise-Defined Functions<\/li>\r\n<\/ul>\r\n<\/div>\r\nIf you\u2019re in the mood for a scary movie, you may want to check out one of the five most popular horror movies of all time\u2014<em data-effect=\"italics\">I am Legend<\/em>, <em data-effect=\"italics\">Hannibal<\/em>, <em data-effect=\"italics\">The Ring<\/em>, <em data-effect=\"italics\">The Grudge<\/em>, and <em data-effect=\"italics\">The Conjuring<\/em>. Figure 1\u00a0shows the amount, in dollars, each of those movies grossed when they were released as well as the ticket sales for horror movies in general by year. Notice that we can use the data to create a function of the amount each movie earned or the total ticket sales for all horror movies by year. In creating various functions using the data, we can identify different independent and dependent variables, and we can analyze the data and the functions to determine the <strong>domain<\/strong> and range. In this section, we will investigate methods for determining the domain and range of functions such as these.\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"975\"]<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2016\/10\/18193523\/CNX_Precalc_Figure_01_02_0012.jpg\" alt=\"Two graphs where the first graph is of the Top-Five Grossing Horror Movies for years 2000-2003 and Market Share of Horror Movies by Year\" width=\"975\" height=\"402\" data-media-type=\"image\/jpg\" \/> <b>Figure 1.<\/b> Based on data compiled by <a href=\"http:\/\/www.the-numbers.com\" target=\"_blank\" rel=\"noopener\">www.the-numbers.com<\/a>.[\/caption]","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>LEARNING OBJECTIVES<\/h3>\n<p>By the end of this lesson, you will be able to:<\/p>\n<ul>\n<li>Find the domain of a function defined by an equation<\/li>\n<li>Write Domain and Range Using Standard Notations<\/li>\n<li>Find Domain and Range from a Graph<\/li>\n<li>Define Domain and Range of Toolkit Functions<\/li>\n<li>Graph Piecewise-Defined Functions<\/li>\n<\/ul>\n<\/div>\n<p>If you\u2019re in the mood for a scary movie, you may want to check out one of the five most popular horror movies of all time\u2014<em data-effect=\"italics\">I am Legend<\/em>, <em data-effect=\"italics\">Hannibal<\/em>, <em data-effect=\"italics\">The Ring<\/em>, <em data-effect=\"italics\">The Grudge<\/em>, and <em data-effect=\"italics\">The Conjuring<\/em>. Figure 1\u00a0shows the amount, in dollars, each of those movies grossed when they were released as well as the ticket sales for horror movies in general by year. Notice that we can use the data to create a function of the amount each movie earned or the total ticket sales for all horror movies by year. In creating various functions using the data, we can identify different independent and dependent variables, and we can analyze the data and the functions to determine the <strong>domain<\/strong> and range. In this section, we will investigate methods for determining the domain and range of functions such as these.<\/p>\n<div style=\"width: 985px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2016\/10\/18193523\/CNX_Precalc_Figure_01_02_0012.jpg\" alt=\"Two graphs where the first graph is of the Top-Five Grossing Horror Movies for years 2000-2003 and Market Share of Horror Movies by Year\" width=\"975\" height=\"402\" data-media-type=\"image\/jpg\" \/><\/p>\n<p class=\"wp-caption-text\"><b>Figure 1.<\/b> Based on data compiled by <a href=\"http:\/\/www.the-numbers.com\" target=\"_blank\" rel=\"noopener\">www.the-numbers.com<\/a>.<\/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-976\">\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>Revision and Adaptation. <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. <strong>Authored by<\/strong>: Abramson, Jay et al.. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2\">http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2<\/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":21,"menu_order":7,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"College Algebra\",\"author\":\"Abramson, Jay et al.\",\"organization\":\"OpenStax\",\"url\":\"http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2\"}]","CANDELA_OUTCOMES_GUID":"417bef86-be86-4ce4-af0a-71660837a3f2","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-976","chapter","type-chapter","status-publish","hentry"],"part":242,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/976","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/wp\/v2\/users\/21"}],"version-history":[{"count":6,"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/976\/revisions"}],"predecessor-version":[{"id":4409,"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/976\/revisions\/4409"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/parts\/242"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/976\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/wp\/v2\/media?parent=976"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=976"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/wp\/v2\/contributor?post=976"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/wp\/v2\/license?post=976"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}