{"id":143,"date":"2023-06-21T13:22:37","date_gmt":"2023-06-21T13:22:37","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/summary-review-6\/"},"modified":"2023-07-04T04:14:25","modified_gmt":"2023-07-04T04:14:25","slug":"summary-review-6","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/summary-review-6\/","title":{"raw":"Summary: Review","rendered":"Summary: Review"},"content":{"raw":"\n\n<h2>Key Concepts<\/h2>\n<ul>\n \t<li>Division by [latex]0[\/latex] is undefined.<\/li>\n \t<li>Values of the input variable that would make the denominator of a rational expression equal to zero must be stated and excluded from the domain of a function containing the expression.<\/li>\n \t<li>To restrict the domain of a rational function, set the denominators each equal to zero. Solve for the variable in each denominator and exclude those solution sets.<\/li>\n \t<li>Taking an even root (e.g., a square root) of a negative number yields an unreal result.\n<ul>\n \t<li>Values of the input variable that would place a negative amount under an even root&nbsp;must be stated and excluded from the domain of a function containing the expression.<\/li>\n<\/ul>\n<\/li>\n \t<li>To restrict the domain of a function containing one radical, set the radicand greater than or equal to zero. Solve for the variable. The resulting solution set is the domain of the function.<\/li>\n \t<li>The domain of a function is read from the x-axis (the horizontal, or independent, axis) of the graph of the function.<\/li>\n \t<li>The range of a function is read from the y-axis (the vertical, or dependent axis) of the graph of the function.<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<dl>\n \t<dt><strong>domain <\/strong><\/dt>\n \t<dd>the set of all possible input into a function<\/dd>\n \t<dt><strong>radical function&nbsp;<\/strong><\/dt>\n \t<dd>a function containing a radical<\/dd>\n \t<dt><strong>radicand&nbsp;<\/strong><\/dt>\n \t<dd>the value underneath the radical sign<\/dd>\n \t<dt><strong>range <\/strong><\/dt>\n \t<dd>the set of all possible output from a function<\/dd>\n \t<dt><strong>rational function&nbsp;<\/strong><\/dt>\n \t<dd>a function containing a rational expression (a fraction)<\/dd>\n<\/dl>\n\n","rendered":"<h2>Key Concepts<\/h2>\n<ul>\n<li>Division by [latex]0[\/latex] is undefined.<\/li>\n<li>Values of the input variable that would make the denominator of a rational expression equal to zero must be stated and excluded from the domain of a function containing the expression.<\/li>\n<li>To restrict the domain of a rational function, set the denominators each equal to zero. Solve for the variable in each denominator and exclude those solution sets.<\/li>\n<li>Taking an even root (e.g., a square root) of a negative number yields an unreal result.\n<ul>\n<li>Values of the input variable that would place a negative amount under an even root&nbsp;must be stated and excluded from the domain of a function containing the expression.<\/li>\n<\/ul>\n<\/li>\n<li>To restrict the domain of a function containing one radical, set the radicand greater than or equal to zero. Solve for the variable. The resulting solution set is the domain of the function.<\/li>\n<li>The domain of a function is read from the x-axis (the horizontal, or independent, axis) of the graph of the function.<\/li>\n<li>The range of a function is read from the y-axis (the vertical, or dependent axis) of the graph of the function.<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<dl>\n<dt><strong>domain <\/strong><\/dt>\n<dd>the set of all possible input into a function<\/dd>\n<dt><strong>radical function&nbsp;<\/strong><\/dt>\n<dd>a function containing a radical<\/dd>\n<dt><strong>radicand&nbsp;<\/strong><\/dt>\n<dd>the value underneath the radical sign<\/dd>\n<dt><strong>range <\/strong><\/dt>\n<dd>the set of all possible output from a function<\/dd>\n<dt><strong>rational function&nbsp;<\/strong><\/dt>\n<dd>a function containing a rational expression (a fraction)<\/dd>\n<\/dl>\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-143\">\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":5,"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-143","chapter","type-chapter","status-publish","hentry"],"part":251,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/143","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":1,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/143\/revisions"}],"predecessor-version":[{"id":628,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/143\/revisions\/628"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/parts\/251"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/143\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/media?parent=143"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=143"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/contributor?post=143"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/license?post=143"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}