{"id":230,"date":"2023-06-21T13:22:46","date_gmt":"2023-06-21T13:22:46","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/review-topics-for-success-8\/"},"modified":"2023-07-04T03:54:53","modified_gmt":"2023-07-04T03:54:53","slug":"review-topics-for-success-8","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/review-topics-for-success-8\/","title":{"raw":"Review Topics for Success: Rational Equations and Proportions","rendered":"Review Topics for Success: Rational Equations and Proportions"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\">\r\n<h3>Learning Outcomes<\/h3>\r\nBy the end of this section, you will be able to:\r\n<ul>\r\n \t<li>Solve a rational formula for a specified variable<\/li>\r\n \t<li>Solve an application using a formula that must be solved for a specified variable<\/li>\r\n \t<li class=\"li2\"><span class=\"s1\">Solve applications by defining and solving rational equations.\u00a0<\/span><\/li>\r\n \t<li class=\"li2\">Solve an application using a formula containing a radical expression<\/li>\r\n \t<li>Graph radical functions using tables and transformations<\/li>\r\n \t<li>Solve an application by writing and solving a proportion<\/li>\r\n<\/ul>\r\n<\/div>\r\nYou've studied how to identify and manipulate rational expressions and radical expressions such as\r\n<p style=\"text-align: center;\">[latex]\\dfrac{5}{x+2}, \\quad \\text{ or } \\quad \\dfrac{x}{x^2-9}, \\quad \\text{ and } \\quad \\sqrt{2x+1}[\/latex].<\/p>\r\nYou've also seen how to solve rational and radical equations (equations in which the variable is contained within one or more rational or radical expressions). This module will extend those concepts to the language of functions, where you'll learn about graphing and applying rational and radical functions to real-world situations.\r\n\r\nTo prepare, it will be important to practice applications of rational and radical equations and see how radical functions are graphed using a few key points. This module includes a problem-solving technique known as variation, which involves writing relationships as proportions in order to solve for an unknown, so it will be helpful to review proportions as well.\r\n\r\nWarm up for this module by refreshing important concepts and skills you'll need for success.\u00a0As you study these review topics, recall that you can also\u00a0return to Algebra Essentials any time you need to refresh the basics.\r\n<div class=\"textbox examples\">\r\n<h3>Recall for success<\/h3>\r\nLook for red boxes like this one throughout the text. They'll show up just in time to give helpful\u00a0reminders of the math you'll need, right where you'll need it.\r\n\r\n<\/div>","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Outcomes<\/h3>\n<p>By the end of this section, you will be able to:<\/p>\n<ul>\n<li>Solve a rational formula for a specified variable<\/li>\n<li>Solve an application using a formula that must be solved for a specified variable<\/li>\n<li class=\"li2\"><span class=\"s1\">Solve applications by defining and solving rational equations.\u00a0<\/span><\/li>\n<li class=\"li2\">Solve an application using a formula containing a radical expression<\/li>\n<li>Graph radical functions using tables and transformations<\/li>\n<li>Solve an application by writing and solving a proportion<\/li>\n<\/ul>\n<\/div>\n<p>You&#8217;ve studied how to identify and manipulate rational expressions and radical expressions such as<\/p>\n<p style=\"text-align: center;\">[latex]\\dfrac{5}{x+2}, \\quad \\text{ or } \\quad \\dfrac{x}{x^2-9}, \\quad \\text{ and } \\quad \\sqrt{2x+1}[\/latex].<\/p>\n<p>You&#8217;ve also seen how to solve rational and radical equations (equations in which the variable is contained within one or more rational or radical expressions). This module will extend those concepts to the language of functions, where you&#8217;ll learn about graphing and applying rational and radical functions to real-world situations.<\/p>\n<p>To prepare, it will be important to practice applications of rational and radical equations and see how radical functions are graphed using a few key points. This module includes a problem-solving technique known as variation, which involves writing relationships as proportions in order to solve for an unknown, so it will be helpful to review proportions as well.<\/p>\n<p>Warm up for this module by refreshing important concepts and skills you&#8217;ll need for success.\u00a0As you study these review topics, recall that you can also\u00a0return to Algebra Essentials any time you need to refresh the basics.<\/p>\n<div class=\"textbox examples\">\n<h3>Recall for success<\/h3>\n<p>Look for red boxes like this one throughout the text. They&#8217;ll show up just in time to give helpful\u00a0reminders of the math you&#8217;ll need, right where you&#8217;ll need it.<\/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-230\">\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><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>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":395986,"menu_order":26,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"\",\"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-230","chapter","type-chapter","status-publish","hentry"],"part":202,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/230","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/users\/395986"}],"version-history":[{"count":4,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/230\/revisions"}],"predecessor-version":[{"id":770,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/230\/revisions\/770"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/parts\/202"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/230\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/media?parent=230"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=230"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/contributor?post=230"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/license?post=230"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}