{"id":132,"date":"2023-06-21T13:22:36","date_gmt":"2023-06-21T13:22:36","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/summary-domain-and-range-of-functions\/"},"modified":"2023-06-21T13:22:36","modified_gmt":"2023-06-21T13:22:36","slug":"summary-domain-and-range-of-functions","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/summary-domain-and-range-of-functions\/","title":{"raw":"Summary: Domain and Range of Functions","rendered":"Summary: Domain and Range of Functions"},"content":{"raw":"\n\n<h2>Key Concepts<\/h2>\n<ul>\n \t<li>The domain of a function includes all real input values that would not cause us to attempt an undefined mathematical operation, such as dividing by zero or taking the square root of a negative number.<\/li>\n \t<li>The domain of a function can be determined by listing the input values of a set of ordered pairs.<\/li>\n \t<li>The domain of a function can also be determined by identifying the input values of a function written as an equation.<\/li>\n \t<li>Interval values represented on a number line can be described using inequality notation, set-builder notation, and interval notation.<\/li>\n \t<li>For many functions, the domain and range can be determined from a graph.<\/li>\n \t<li>An understanding of toolkit functions can be used to find the domain and range of related functions.<\/li>\n \t<li>A piecewise function is described by more than one formula.<\/li>\n \t<li>A piecewise function can be graphed using each algebraic formula on its assigned subdomain.<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<dl id=\"fs-id1165135445751\" class=\"definition\">\n \t<dt><strong>interval notation<\/strong><\/dt>\n \t<dd id=\"fs-id1165135190252\">a method of describing a set that includes all numbers between a lower limit and an upper limit; the lower and upper values are listed between brackets or parentheses, a square bracket indicating inclusion in the set, and a parenthesis indicating exclusion<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135487256\" class=\"definition\">\n \t<dt><strong>piecewise function<\/strong><\/dt>\n \t<dd id=\"fs-id1165137452169\">a function in which more than one formula is used to define the output<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137863188\" class=\"definition\">\n \t<dt><strong>set-builder notation<\/strong><\/dt>\n \t<dd id=\"fs-id1165137863193\">a method of describing a set by a rule that all of its members obey; it takes the form [latex]\\left\\{x|\\text{statement about }x\\right\\}[\/latex]<\/dd>\n<\/dl>\n\n","rendered":"<h2>Key Concepts<\/h2>\n<ul>\n<li>The domain of a function includes all real input values that would not cause us to attempt an undefined mathematical operation, such as dividing by zero or taking the square root of a negative number.<\/li>\n<li>The domain of a function can be determined by listing the input values of a set of ordered pairs.<\/li>\n<li>The domain of a function can also be determined by identifying the input values of a function written as an equation.<\/li>\n<li>Interval values represented on a number line can be described using inequality notation, set-builder notation, and interval notation.<\/li>\n<li>For many functions, the domain and range can be determined from a graph.<\/li>\n<li>An understanding of toolkit functions can be used to find the domain and range of related functions.<\/li>\n<li>A piecewise function is described by more than one formula.<\/li>\n<li>A piecewise function can be graphed using each algebraic formula on its assigned subdomain.<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<dl id=\"fs-id1165135445751\" class=\"definition\">\n<dt><strong>interval notation<\/strong><\/dt>\n<dd id=\"fs-id1165135190252\">a method of describing a set that includes all numbers between a lower limit and an upper limit; the lower and upper values are listed between brackets or parentheses, a square bracket indicating inclusion in the set, and a parenthesis indicating exclusion<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135487256\" class=\"definition\">\n<dt><strong>piecewise function<\/strong><\/dt>\n<dd id=\"fs-id1165137452169\">a function in which more than one formula is used to define the output<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137863188\" class=\"definition\">\n<dt><strong>set-builder notation<\/strong><\/dt>\n<dd id=\"fs-id1165137863193\">a method of describing a set by a rule that all of its members obey; it takes the form [latex]\\left\\{x|\\text{statement about }x\\right\\}[\/latex]<\/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-132\">\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":395986,"menu_order":17,"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-132","chapter","type-chapter","status-publish","hentry"],"part":115,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/132","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":0,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/132\/revisions"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/parts\/115"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/132\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/media?parent=132"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=132"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/contributor?post=132"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/license?post=132"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}