{"id":1992,"date":"2024-06-27T00:43:25","date_gmt":"2024-06-27T00:43:25","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/?post_type=chapter&#038;p=1992"},"modified":"2025-01-15T15:11:30","modified_gmt":"2025-01-15T15:11:30","slug":"module-10-cheat-sheet","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/chapter\/module-10-cheat-sheet\/","title":{"raw":"Rational and Radical Functions: Cheat Sheet","rendered":"Rational and Radical Functions: Cheat Sheet"},"content":{"raw":"<p style=\"text-align: right;\"><a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/College+Algebra+LOHM\/Cheat+Sheets\/College+Algebra+Cheat+Sheet+M10_+Rational+and+Radical+Functions.pdf\" target=\"_blank\" rel=\"noopener\"><span style=\"font-size: 14pt;\">Download a PDF of this page here.<\/span><\/a><\/p>\r\n<p style=\"text-align: right;\"><span style=\"font-size: 14pt;\">Download the Spanish version here.<\/span><\/p>\r\n\r\n<h2>Essential Concepts<\/h2>\r\n<h3>Rational Functions<\/h3>\r\n<ul>\r\n \t<li>A rational function is a function that can be written as the quotient of two polynomial functions.<\/li>\r\n \t<li>We can use arrow notation to describe local behavior and end behavior of rational functions.<\/li>\r\n \t<li>The vertical asymptotes of a rational function will occur where the denominator of the function is equal to zero and the numerator is not zero.<\/li>\r\n \t<li>A hole or removable discontinuity might occur in the graph of a rational function if an input causes both numerator and denominator to be zero.<\/li>\r\n \t<li>The domain of a rational function includes all real numbers except those that cause the denominator to equal zero.<\/li>\r\n \t<li>The\u00a0horizontal asymptote\u00a0of a rational function can be determined by looking at the degrees of the numerator and denominator.\r\n<ul id=\"fs-id1165137722720\">\r\n \t<li><strong>Case 1:<\/strong>\u00a0Degree of numerator\u00a0<em>is less than<\/em> degree of denominator: horizontal asymptote at [latex]y = 0[\/latex].<\/li>\r\n \t<li><strong>Case 2<\/strong>: Degree of numerator\u00a0<em>is greater than degree of denominator by one<\/em>: no horizontal asymptote; slant asymptote.\r\n<ul>\r\n \t<li>If the degree of the numerator is greater than the degree of the denominator by\u00a0<em>more than one<\/em>, the end behavior of the function\u2019s graph will mimic that of the graph of the reduced ratio of leading terms.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong>Case 3<\/strong>: Degree of numerator\u00a0<em>is equal to<\/em>\u00a0degree of denominator: horizontal asymptote at ratio of leading coefficients.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>A rational function\u2019s end behavior will mirror that of the ratio of the leading terms of the numerator and denominator functions.<\/li>\r\n \t<li>Graph rational functions by finding the intercepts, behavior at the intercepts and asymptotes, and end behavior.<\/li>\r\n \t<li>A rational function will not have a [latex]y[\/latex]-intercept if the function is not defined at zero.<\/li>\r\n \t<li>The [latex]x[\/latex]-intercept(s) of a rational function can only occur when the numerator of the rational function is equal to zero.<\/li>\r\n \t<li>If a rational function has [latex]x[\/latex]-intercepts at [latex]x={x}_{1},{x}_{2},\\dots ,{x}_{n}[\/latex], vertical asymptotes at [latex]x={v}_{1},{v}_{2},\\dots ,{v}_{m}[\/latex], and no [latex]{x}_{i}=\\text{any }{v}_{j}[\/latex], then the function can be written in the form\u00a0[latex]f\\left(x\\right)=a\\dfrac{{\\left(x-{x}_{1}\\right)}^{{p}_{1}}{\\left(x-{x}_{2}\\right)}^{{p}_{2}}\\cdots {\\left(x-{x}_{n}\\right)}^{{p}_{n}}}{{\\left(x-{v}_{1}\\right)}^{{q}_{1}}{\\left(x-{v}_{2}\\right)}^{{q}_{2}}\\cdots {\\left(x-{v}_{m}\\right)}^{{q}_{n}}}[\/latex]<\/li>\r\n<\/ul>\r\n<h3>Radical Functions<\/h3>\r\n<ul>\r\n \t<li>A\u00a0<strong>radical function<\/strong>\u00a0is a function that involves the use of a radical (root) symbol to indicate the root of a number or expression.<\/li>\r\n \t<li>The inverse of a quadratic function is a square root function.<\/li>\r\n \t<li>To find the inverse of certain functions, we must restrict the function to a domain on which it will be one-to-one.\r\n<ul>\r\n \t<li>For even roots (e.g., square roots), the expression inside the radical must be non-negative, as you cannot take the even root of a negative number in the real number system.<\/li>\r\n \t<li>For odd roots (e.g., cube roots), the expression inside the radical can be any real number.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>Domain<span style=\"font-family: 'Public Sans', -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Oxygen-Sans, Ubuntu, Cantarell, 'Helvetica Neue', sans-serif;\">: The domain of a radical function depends on the index [latex]n[\/latex]<\/span><\/li>\r\n \t<li>Range: The range of a radical function varies based on the specific function and its domain.<\/li>\r\n \t<li>To find the inverse of certain functions, we must restrict the function to a domain on which it will be one-to-one.<\/li>\r\n \t<li>When finding the inverse of a radical function, we need a restriction on the domain of the answer.<\/li>\r\n \t<li>Inverse and radical functions can be used to solve application problems.<\/li>\r\n<\/ul>\r\n<h3><strong>Variation<\/strong><\/h3>\r\n<ul>\r\n \t<li>A relationship where one quantity is a constant multiplied by another quantity is called direct variation.<\/li>\r\n \t<li>Two variables that are directly proportional to one another will have a constant ratio.<\/li>\r\n \t<li>A relationship where one quantity is a constant divided by another quantity is called inverse variation.<\/li>\r\n \t<li>Two variables that are inversely proportional to one another will have a constant multiple.<\/li>\r\n \t<li>In many problems, a variable varies directly or inversely with multiple variables. We call this type of relationship joint variation.<\/li>\r\n<\/ul>\r\n<h2>Key Equations<\/h2>\r\n<table id=\"eip-id1362369\" style=\"width: 100.836%;\" summary=\"..\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 19.2844%;\"><strong>Rational Function<\/strong><\/td>\r\n<td style=\"width: 81.093%;\">[latex]f\\left(x\\right)=\\dfrac{P\\left(x\\right)}{Q\\left(x\\right)}=\\dfrac{{a}_{p}{x}^{p}+{a}_{p - 1}{x}^{p - 1}+...+{a}_{1}x+{a}_{0}}{{b}_{q}{x}^{q}+{b}_{q - 1}{x}^{q - 1}+...+{b}_{1}x+{b}_{0}}, Q\\left(x\\right)\\ne 0[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 19.2844%;\"><strong>Direct variation<\/strong><\/td>\r\n<td style=\"width: 81.093%;\">[latex]y=k{x}^{n},k\\text{ is a nonzero constant}[\/latex].<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 19.2844%;\"><strong>Inverse variation<\/strong><\/td>\r\n<td style=\"width: 81.093%;\">[latex]y=\\dfrac{k}{{x}^{n}},k\\text{ is a nonzero constant}[\/latex].<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h2>Glossary<\/h2>\r\n<dl id=\"fs-id1165137758530\" class=\"definition\">\r\n \t<dt><strong>arrow notation<\/strong><\/dt>\r\n \t<dd id=\"fs-id1165135154402\">a way to symbolically represent the local and end behavior of a function by using arrows to indicate that an input or output approaches a value<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1165137735724\" class=\"definition\">\r\n \t<dt><strong>constant of variation<\/strong><\/dt>\r\n \t<dd id=\"fs-id1165137735729\">the non-zero value [latex]k[\/latex]\u00a0that helps define the relationship between variables in direct or inverse variation<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1165137762202\" class=\"definition\">\r\n \t<dt><strong>direct variation<\/strong><\/dt>\r\n \t<dd id=\"fs-id1165137762208\">the relationship between two variables that are a constant multiple of each other; as one quantity increases, so does the other<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1165135154407\" class=\"definition\">\r\n \t<dt><strong>horizontal asymptote<\/strong><\/dt>\r\n \t<dd id=\"fs-id1165135154413\">a horizontal line [latex]y=b[\/latex]\u00a0where the graph approaches the line as the inputs increase or decrease without bound.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1165137462046\" class=\"definition\">\r\n \t<dt><strong>inverse variation<\/strong><\/dt>\r\n \t<dd id=\"fs-id1165137462052\">the relationship between two variables in which the product of the variables is a constant<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1165135501040\" class=\"definition\">\r\n \t<dt><strong>inversely proportional<\/strong><\/dt>\r\n \t<dd id=\"fs-id1165137874542\">a relationship where one quantity is a constant divided by the other quantity; as one quantity increases, the other decreases<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1165135169260\" class=\"definition\">\r\n \t<dt><strong>invertible function<\/strong><\/dt>\r\n \t<dd id=\"fs-id1165135169263\">any function that has an inverse function<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1165137874546\" class=\"definition\">\r\n \t<dt><strong>joint variation<\/strong><\/dt>\r\n \t<dd id=\"fs-id1165135696715\">a relationship where a variable varies directly or inversely with multiple variables<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1165135192626\" class=\"definition\">\r\n \t<dt><strong>rational function<\/strong><\/dt>\r\n \t<dd id=\"fs-id1165134401081\">a function that can be written as the ratio of two polynomials<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1165134401085\" class=\"definition\">\r\n \t<dt><strong>removable discontinuity<\/strong><\/dt>\r\n \t<dd id=\"fs-id1165134401090\">a single point at which a function is undefined that, if filled in, would make the function continuous; it appears as a hole on the graph of a function<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1165135696718\" class=\"definition\">\r\n \t<dt><strong>varies directly<\/strong><\/dt>\r\n \t<dd id=\"fs-id1165137432955\">a relationship where one quantity is a constant multiplied by the other quantity<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1165137432958\" class=\"definition\">\r\n \t<dt><strong>varies inversely<\/strong><\/dt>\r\n \t<dd id=\"fs-id1165135439853\">a relationship where one quantity is a constant divided by the other quantity<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1165137426312\" class=\"definition\">\r\n \t<dt><strong>vertical asymptote<\/strong><\/dt>\r\n \t<dd id=\"fs-id1165137426317\">a vertical line [latex]x=a[\/latex] where the graph tends toward positive or negative infinity as the inputs approach [latex]a[\/latex]<\/dd>\r\n<\/dl>","rendered":"<p style=\"text-align: right;\"><a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/College+Algebra+LOHM\/Cheat+Sheets\/College+Algebra+Cheat+Sheet+M10_+Rational+and+Radical+Functions.pdf\" target=\"_blank\" rel=\"noopener\"><span style=\"font-size: 14pt;\">Download a PDF of this page here.<\/span><\/a><\/p>\n<p style=\"text-align: right;\"><span style=\"font-size: 14pt;\">Download the Spanish version here.<\/span><\/p>\n<h2>Essential Concepts<\/h2>\n<h3>Rational Functions<\/h3>\n<ul>\n<li>A rational function is a function that can be written as the quotient of two polynomial functions.<\/li>\n<li>We can use arrow notation to describe local behavior and end behavior of rational functions.<\/li>\n<li>The vertical asymptotes of a rational function will occur where the denominator of the function is equal to zero and the numerator is not zero.<\/li>\n<li>A hole or removable discontinuity might occur in the graph of a rational function if an input causes both numerator and denominator to be zero.<\/li>\n<li>The domain of a rational function includes all real numbers except those that cause the denominator to equal zero.<\/li>\n<li>The\u00a0horizontal asymptote\u00a0of a rational function can be determined by looking at the degrees of the numerator and denominator.\n<ul id=\"fs-id1165137722720\">\n<li><strong>Case 1:<\/strong>\u00a0Degree of numerator\u00a0<em>is less than<\/em> degree of denominator: horizontal asymptote at [latex]y = 0[\/latex].<\/li>\n<li><strong>Case 2<\/strong>: Degree of numerator\u00a0<em>is greater than degree of denominator by one<\/em>: no horizontal asymptote; slant asymptote.\n<ul>\n<li>If the degree of the numerator is greater than the degree of the denominator by\u00a0<em>more than one<\/em>, the end behavior of the function\u2019s graph will mimic that of the graph of the reduced ratio of leading terms.<\/li>\n<\/ul>\n<\/li>\n<li><strong>Case 3<\/strong>: Degree of numerator\u00a0<em>is equal to<\/em>\u00a0degree of denominator: horizontal asymptote at ratio of leading coefficients.<\/li>\n<\/ul>\n<\/li>\n<li>A rational function\u2019s end behavior will mirror that of the ratio of the leading terms of the numerator and denominator functions.<\/li>\n<li>Graph rational functions by finding the intercepts, behavior at the intercepts and asymptotes, and end behavior.<\/li>\n<li>A rational function will not have a [latex]y[\/latex]-intercept if the function is not defined at zero.<\/li>\n<li>The [latex]x[\/latex]-intercept(s) of a rational function can only occur when the numerator of the rational function is equal to zero.<\/li>\n<li>If a rational function has [latex]x[\/latex]-intercepts at [latex]x={x}_{1},{x}_{2},\\dots ,{x}_{n}[\/latex], vertical asymptotes at [latex]x={v}_{1},{v}_{2},\\dots ,{v}_{m}[\/latex], and no [latex]{x}_{i}=\\text{any }{v}_{j}[\/latex], then the function can be written in the form\u00a0[latex]f\\left(x\\right)=a\\dfrac{{\\left(x-{x}_{1}\\right)}^{{p}_{1}}{\\left(x-{x}_{2}\\right)}^{{p}_{2}}\\cdots {\\left(x-{x}_{n}\\right)}^{{p}_{n}}}{{\\left(x-{v}_{1}\\right)}^{{q}_{1}}{\\left(x-{v}_{2}\\right)}^{{q}_{2}}\\cdots {\\left(x-{v}_{m}\\right)}^{{q}_{n}}}[\/latex]<\/li>\n<\/ul>\n<h3>Radical Functions<\/h3>\n<ul>\n<li>A\u00a0<strong>radical function<\/strong>\u00a0is a function that involves the use of a radical (root) symbol to indicate the root of a number or expression.<\/li>\n<li>The inverse of a quadratic function is a square root function.<\/li>\n<li>To find the inverse of certain functions, we must restrict the function to a domain on which it will be one-to-one.\n<ul>\n<li>For even roots (e.g., square roots), the expression inside the radical must be non-negative, as you cannot take the even root of a negative number in the real number system.<\/li>\n<li>For odd roots (e.g., cube roots), the expression inside the radical can be any real number.<\/li>\n<\/ul>\n<\/li>\n<li>Domain<span style=\"font-family: 'Public Sans', -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Oxygen-Sans, Ubuntu, Cantarell, 'Helvetica Neue', sans-serif;\">: The domain of a radical function depends on the index [latex]n[\/latex]<\/span><\/li>\n<li>Range: The range of a radical function varies based on the specific function and its domain.<\/li>\n<li>To find the inverse of certain functions, we must restrict the function to a domain on which it will be one-to-one.<\/li>\n<li>When finding the inverse of a radical function, we need a restriction on the domain of the answer.<\/li>\n<li>Inverse and radical functions can be used to solve application problems.<\/li>\n<\/ul>\n<h3><strong>Variation<\/strong><\/h3>\n<ul>\n<li>A relationship where one quantity is a constant multiplied by another quantity is called direct variation.<\/li>\n<li>Two variables that are directly proportional to one another will have a constant ratio.<\/li>\n<li>A relationship where one quantity is a constant divided by another quantity is called inverse variation.<\/li>\n<li>Two variables that are inversely proportional to one another will have a constant multiple.<\/li>\n<li>In many problems, a variable varies directly or inversely with multiple variables. We call this type of relationship joint variation.<\/li>\n<\/ul>\n<h2>Key Equations<\/h2>\n<table id=\"eip-id1362369\" style=\"width: 100.836%;\" summary=\"..\">\n<tbody>\n<tr>\n<td style=\"width: 19.2844%;\"><strong>Rational Function<\/strong><\/td>\n<td style=\"width: 81.093%;\">[latex]f\\left(x\\right)=\\dfrac{P\\left(x\\right)}{Q\\left(x\\right)}=\\dfrac{{a}_{p}{x}^{p}+{a}_{p - 1}{x}^{p - 1}+...+{a}_{1}x+{a}_{0}}{{b}_{q}{x}^{q}+{b}_{q - 1}{x}^{q - 1}+...+{b}_{1}x+{b}_{0}}, Q\\left(x\\right)\\ne 0[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 19.2844%;\"><strong>Direct variation<\/strong><\/td>\n<td style=\"width: 81.093%;\">[latex]y=k{x}^{n},k\\text{ is a nonzero constant}[\/latex].<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 19.2844%;\"><strong>Inverse variation<\/strong><\/td>\n<td style=\"width: 81.093%;\">[latex]y=\\dfrac{k}{{x}^{n}},k\\text{ is a nonzero constant}[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Glossary<\/h2>\n<dl id=\"fs-id1165137758530\" class=\"definition\">\n<dt><strong>arrow notation<\/strong><\/dt>\n<dd id=\"fs-id1165135154402\">a way to symbolically represent the local and end behavior of a function by using arrows to indicate that an input or output approaches a value<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137735724\" class=\"definition\">\n<dt><strong>constant of variation<\/strong><\/dt>\n<dd id=\"fs-id1165137735729\">the non-zero value [latex]k[\/latex]\u00a0that helps define the relationship between variables in direct or inverse variation<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137762202\" class=\"definition\">\n<dt><strong>direct variation<\/strong><\/dt>\n<dd id=\"fs-id1165137762208\">the relationship between two variables that are a constant multiple of each other; as one quantity increases, so does the other<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135154407\" class=\"definition\">\n<dt><strong>horizontal asymptote<\/strong><\/dt>\n<dd id=\"fs-id1165135154413\">a horizontal line [latex]y=b[\/latex]\u00a0where the graph approaches the line as the inputs increase or decrease without bound.<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137462046\" class=\"definition\">\n<dt><strong>inverse variation<\/strong><\/dt>\n<dd id=\"fs-id1165137462052\">the relationship between two variables in which the product of the variables is a constant<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135501040\" class=\"definition\">\n<dt><strong>inversely proportional<\/strong><\/dt>\n<dd id=\"fs-id1165137874542\">a relationship where one quantity is a constant divided by the other quantity; as one quantity increases, the other decreases<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135169260\" class=\"definition\">\n<dt><strong>invertible function<\/strong><\/dt>\n<dd id=\"fs-id1165135169263\">any function that has an inverse function<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137874546\" class=\"definition\">\n<dt><strong>joint variation<\/strong><\/dt>\n<dd id=\"fs-id1165135696715\">a relationship where a variable varies directly or inversely with multiple variables<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135192626\" class=\"definition\">\n<dt><strong>rational function<\/strong><\/dt>\n<dd id=\"fs-id1165134401081\">a function that can be written as the ratio of two polynomials<\/dd>\n<\/dl>\n<dl id=\"fs-id1165134401085\" class=\"definition\">\n<dt><strong>removable discontinuity<\/strong><\/dt>\n<dd id=\"fs-id1165134401090\">a single point at which a function is undefined that, if filled in, would make the function continuous; it appears as a hole on the graph of a function<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135696718\" class=\"definition\">\n<dt><strong>varies directly<\/strong><\/dt>\n<dd id=\"fs-id1165137432955\">a relationship where one quantity is a constant multiplied by the other quantity<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137432958\" class=\"definition\">\n<dt><strong>varies inversely<\/strong><\/dt>\n<dd id=\"fs-id1165135439853\">a relationship where one quantity is a constant divided by the other quantity<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137426312\" class=\"definition\">\n<dt><strong>vertical asymptote<\/strong><\/dt>\n<dd id=\"fs-id1165137426317\">a vertical line [latex]x=a[\/latex] where the graph tends toward positive or negative infinity as the inputs approach [latex]a[\/latex]<\/dd>\n<\/dl>\n","protected":false},"author":12,"menu_order":1,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":232,"module-header":"cheat_sheet","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1992"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/users\/12"}],"version-history":[{"count":14,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1992\/revisions"}],"predecessor-version":[{"id":7353,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1992\/revisions\/7353"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/parts\/232"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1992\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/media?parent=1992"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=1992"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/contributor?post=1992"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/license?post=1992"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}