{"id":864,"date":"2015-11-12T18:37:58","date_gmt":"2015-11-12T18:37:58","guid":{"rendered":"https:\/\/courses.candelalearning.com\/collegealgebra1xmaster\/?post_type=chapter&#038;p=864"},"modified":"2015-11-12T18:37:58","modified_gmt":"2015-11-12T18:37:58","slug":"introduction-to-rates-of-change-and-behaviors-of-graphs","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/atd-sanjac-collegealgebra\/chapter\/introduction-to-rates-of-change-and-behaviors-of-graphs\/","title":{"raw":"Introduction to Rates of Change and Behaviors of Graphs","rendered":"Introduction to Rates of Change and Behaviors of Graphs"},"content":{"raw":"<div data-type=\"document-title\">\n<div class=\"bcc-box bcc-highlight\">\n\n<h3>LEARNING OBJECTIVES<\/h3>\n\nBy the end of this lesson, you will be able to:\n\n<ul><li>Find the average rate of change of a function.<\/li>\n\t<li>Use a graph to determine where a function is increasing, decreasing, or constant.<\/li>\n\t<li>Use a graph to locate local maxima and local minima.<\/li>\n\t<li>Use a graph to locate the absolute maximum and absolute minimum.<\/li>\n<\/ul><\/div>\n<p id=\"fs-id1165135194500\">Gasoline costs have experienced some wild fluctuations over the last several decades. The table below[footnote]http:\/\/www.eia.gov\/totalenergy\/data\/annual\/showtext.cfm?t=ptb0524. Accessed 3\/5\/2014.[\/footnote]\u00a0lists the average cost, in dollars, of a gallon of gasoline for the years 2005\u20132012. The cost of gasoline can be considered as a function of year.<\/p>\n\n<table summary=\"Two rows and nine columns. The first row is labeled,\"><colgroup><col data-width=\"40\"\/><col data-width=\"40\"\/><col data-width=\"40\"\/><col data-width=\"40\"\/><col data-width=\"40\"\/><col data-width=\"40\"\/><col data-width=\"40\"\/><col data-width=\"40\"\/><col data-width=\"40\"\/><\/colgroup><tbody><tr><td data-align=\"center\"><strong>[latex]y[\/latex]<\/strong><\/td>\n<td data-align=\"center\">2005<\/td>\n<td data-align=\"center\">2006<\/td>\n<td data-align=\"center\">2007<\/td>\n<td data-align=\"center\">2008<\/td>\n<td data-align=\"center\">2009<\/td>\n<td data-align=\"center\">2010<\/td>\n<td data-align=\"center\">2011<\/td>\n<td data-align=\"center\">2012<\/td>\n<\/tr><tr><td data-align=\"center\"><strong>[latex]C\\left(y\\right)[\/latex]<\/strong><\/td>\n<td data-align=\"center\">2.31<\/td>\n<td data-align=\"center\">2.62<\/td>\n<td data-align=\"center\">2.84<\/td>\n<td data-align=\"center\">3.30<\/td>\n<td data-align=\"center\">2.41<\/td>\n<td data-align=\"center\">2.84<\/td>\n<td data-align=\"center\">3.58<\/td>\n<td data-align=\"center\">3.68<\/td>\n<\/tr><\/tbody><\/table><p id=\"fs-id1165133097252\">If we were interested only in how the gasoline prices changed between 2005 and 2012, we could compute that the cost per gallon had increased from $2.31 to $3.68, an increase of $1.37. While this is interesting, it might be more useful to look at how much the price changed <em data-effect=\"italics\">per year<\/em>. In this section, we will investigate changes such as these.<\/p><\/div>","rendered":"<div data-type=\"document-title\">\n<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 average rate of change of a function.<\/li>\n<li>Use a graph to determine where a function is increasing, decreasing, or constant.<\/li>\n<li>Use a graph to locate local maxima and local minima.<\/li>\n<li>Use a graph to locate the absolute maximum and absolute minimum.<\/li>\n<\/ul>\n<\/div>\n<p id=\"fs-id1165135194500\">Gasoline costs have experienced some wild fluctuations over the last several decades. The table below<a class=\"footnote\" title=\"http:\/\/www.eia.gov\/totalenergy\/data\/annual\/showtext.cfm?t=ptb0524. Accessed 3\/5\/2014.\" id=\"return-footnote-864-1\" href=\"#footnote-864-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a>\u00a0lists the average cost, in dollars, of a gallon of gasoline for the years 2005\u20132012. The cost of gasoline can be considered as a function of year.<\/p>\n<table summary=\"Two rows and nine columns. The first row is labeled,\">\n<colgroup>\n<col data-width=\"40\" \/>\n<col data-width=\"40\" \/>\n<col data-width=\"40\" \/>\n<col data-width=\"40\" \/>\n<col data-width=\"40\" \/>\n<col data-width=\"40\" \/>\n<col data-width=\"40\" \/>\n<col data-width=\"40\" \/>\n<col data-width=\"40\" \/><\/colgroup>\n<tbody>\n<tr>\n<td data-align=\"center\"><strong>[latex]y[\/latex]<\/strong><\/td>\n<td data-align=\"center\">2005<\/td>\n<td data-align=\"center\">2006<\/td>\n<td data-align=\"center\">2007<\/td>\n<td data-align=\"center\">2008<\/td>\n<td data-align=\"center\">2009<\/td>\n<td data-align=\"center\">2010<\/td>\n<td data-align=\"center\">2011<\/td>\n<td data-align=\"center\">2012<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\"><strong>[latex]C\\left(y\\right)[\/latex]<\/strong><\/td>\n<td data-align=\"center\">2.31<\/td>\n<td data-align=\"center\">2.62<\/td>\n<td data-align=\"center\">2.84<\/td>\n<td data-align=\"center\">3.30<\/td>\n<td data-align=\"center\">2.41<\/td>\n<td data-align=\"center\">2.84<\/td>\n<td data-align=\"center\">3.58<\/td>\n<td data-align=\"center\">3.68<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1165133097252\">If we were interested only in how the gasoline prices changed between 2005 and 2012, we could compute that the cost per gallon had increased from $2.31 to $3.68, an increase of $1.37. While this is interesting, it might be more useful to look at how much the price changed <em data-effect=\"italics\">per year<\/em>. In this section, we will investigate changes such as these.<\/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-864\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Precalculus. <strong>Authored by<\/strong>: Jay Abramson, et al.. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175\">http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175<\/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\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175.<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section><hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-864-1\">http:\/\/www.eia.gov\/totalenergy\/data\/annual\/showtext.cfm?t=ptb0524. Accessed 3\/5\/2014. <a href=\"#return-footnote-864-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":276,"menu_order":1,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Precalculus\",\"author\":\"Jay Abramson, et al.\",\"organization\":\"OpenStax\",\"url\":\"http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download For Free at : http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175.\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-864","chapter","type-chapter","status-publish","hentry"],"part":863,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/atd-sanjac-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/864","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/atd-sanjac-collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/atd-sanjac-collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/atd-sanjac-collegealgebra\/wp-json\/wp\/v2\/users\/276"}],"version-history":[{"count":1,"href":"https:\/\/courses.lumenlearning.com\/atd-sanjac-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/864\/revisions"}],"predecessor-version":[{"id":2503,"href":"https:\/\/courses.lumenlearning.com\/atd-sanjac-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/864\/revisions\/2503"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/atd-sanjac-collegealgebra\/wp-json\/pressbooks\/v2\/parts\/863"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/atd-sanjac-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/864\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/atd-sanjac-collegealgebra\/wp-json\/wp\/v2\/media?parent=864"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/atd-sanjac-collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=864"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/atd-sanjac-collegealgebra\/wp-json\/wp\/v2\/contributor?post=864"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/atd-sanjac-collegealgebra\/wp-json\/wp\/v2\/license?post=864"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}