{"id":1216,"date":"2023-06-05T14:49:24","date_gmt":"2023-06-05T14:49:24","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/tulsacc-math1613\/chapter\/learning-outcomes\/"},"modified":"2023-06-05T14:49:24","modified_gmt":"2023-06-05T14:49:24","slug":"learning-outcomes","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/tulsacc-math1613\/chapter\/learning-outcomes\/","title":{"raw":"Learning Outcomes","rendered":"Learning Outcomes"},"content":{"raw":"\n<img class=\"aligncenter wp-image-254\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2025\/2017\/07\/01225024\/outcomes.jpg\" alt=\"icon of a magnifying glass over a list\" width=\"200\" height=\"201\">\n\nThe content, assignments, and assessments for Precalculus are aligned to the following learning outcomes. A full list of course learning outcomes can be viewed here: <a href=\"https:\/\/docs.google.com\/spreadsheets\/d\/1YC7umNfGS835ZUHcDM4fixul7fVy-79MxI1aWiTLJno\/edit?usp=sharing\" target=\"_blank\" rel=\"noopener\">Precalculus Learning Outcomes<\/a>.\n<h2>Module 1: Introduction to Functions<\/h2>\n<h3>Describe properties of functions and their relationships<\/h3>\n<ul>\n \t<li>Identify and evaluate functions<\/li>\n \t<li>Calculate the domain and range of a function<\/li>\n \t<li>Describe change behaviors of graphs<\/li>\n \t<li>Evaluate composite functions<\/li>\n \t<li>Transform functions<\/li>\n \t<li>Solve absolute value functions<\/li>\n \t<li>Find inverse functions<\/li>\n<\/ul>\n<h2>Module 2: Linear Functions<\/h2>\n<h3>Understand linear functions, their graphs, and how they relate to data<\/h3>\n<ul>\n \t<li>Evaluate linear functions<\/li>\n \t<li>Graph linear functions<\/li>\n \t<li>Model real world scenarios with linear functions<\/li>\n \t<li>Use linear models of data to make predictions<\/li>\n<\/ul>\n<h2>Module 3:&nbsp;<span class=\"os-text\">Polynomial and Rational Functions<\/span><\/h2>\n<h3>Evaluate polynomial and rational functions and their graphs<\/h3>\n<ul>\n \t<li>Simplify complex number expressions<\/li>\n \t<li>Understand quadratic functions<\/li>\n \t<li>Identify power functions and polynomial functions<\/li>\n \t<li>Graph polynomial functions<\/li>\n \t<li>Divide polynomial functions<\/li>\n \t<li>Find the zeros of polynomial equations<\/li>\n \t<li>Graph rational functions<\/li>\n \t<li>Find inverse functions<\/li>\n \t<li>Solve direct, indirect, and joint variation problems<\/li>\n<\/ul>\n<h2>Module 4:&nbsp;<span class=\"os-text\">Exponential and Logarithmic Functions<\/span><\/h2>\n<h3>Model growth and decay patterns with exponential and logarithmic functions<\/h3>\n<ul>\n \t<li>Evaluate exponential functions<\/li>\n \t<li>Graph exponential functions<\/li>\n \t<li>Use logarithmic functions<\/li>\n \t<li>Graph logarithmic functions<\/li>\n \t<li>Expand and condense logarithmic expressions<\/li>\n \t<li>Solve exponential and logarithmic equations<\/li>\n \t<li>Use exponential and logarithmic models<\/li>\n \t<li>Fit exponential models to data<\/li>\n<\/ul>\n<h2>Module 5: Systems of Equations and Inequalities<\/h2>\n<h3>Evaluate systems of linear and non-linear equations with both two and three variables<\/h3>\n<ul>\n \t<li>Solve systems of linear equations in two variables<\/li>\n \t<li>Solve systems of linear equations in three variables<\/li>\n \t<li>Solve and graph systems of nonlinear equations and inequalities<\/li>\n \t<li>Decompose partial fractions<\/li>\n \t<li>Evaluate matrices and matrix operations<\/li>\n \t<li>Write and solve systems with Gaussian Elimination<\/li>\n \t<li>Solve systems with inverses<\/li>\n \t<li>Solve systems with Cramer's rule<\/li>\n<\/ul>\n<h2>Module 6: Sequences, Probability, and Counting Theory<\/h2>\n<h3>Solve sequence and counting problems<\/h3>\n<ul>\n \t<li>Write the terms of a sequence<\/li>\n \t<li>Evaluate arithmetic sequences<\/li>\n \t<li>Evaluate geometric sequences<\/li>\n \t<li>Find the terms of a series<\/li>\n \t<li>Solve counting problems<\/li>\n \t<li>Use the binomial theorem<\/li>\n \t<li>Compute probabilities<\/li>\n<\/ul>\n<h2>Module 7: Trigonometric Functions<\/h2>\n<h3>Evaluate trigonometric functions using angles and right triangles<\/h3>\n<ul>\n \t<li>Find and use angles<\/li>\n \t<li>Evaluate sine and cosine functions<\/li>\n \t<li>Understand other trigonometric functions<\/li>\n \t<li>Use right triangle trigonometry<\/li>\n<\/ul>\n<h2>Module 8: Periodic Functions<\/h2>\n<h3>Analyze the graphs of trigonometric functions<\/h3>\n<ul>\n \t<li>Graph sine and cosine functions<\/li>\n \t<li>Analyze and graph other trigonometric functions<\/li>\n \t<li>Use inverse trigonometric functions<\/li>\n<\/ul>\n<h2>Module 9: Trigonometric Identities and Equations<\/h2>\n<h3>Solve trigonometric equations using identities<\/h3>\n<ul>\n \t<li>Solve trigonometric equations with identities<\/li>\n \t<li>Use sum and difference formulas<\/li>\n \t<li>Use double-angle, half-angle, and reduction formulas<\/li>\n \t<li>Use sum-to-product and product-to-sum formulas<\/li>\n \t<li>Solve trigonometric equations<\/li>\n \t<li>Model trigonometric equations<\/li>\n<\/ul>\n<h2>Module 10: Further Applications of Trigonometry<\/h2>\n<h3>Apply trigonometric rules to evaluate more complex graphs and equations<\/h3>\n<ul>\n \t<li>Solve non-right triangles using the Law of Sines<\/li>\n \t<li>Solve non-right triangles using the Law of Cosines<\/li>\n \t<li>Identify and use polar coordinates<\/li>\n \t<li>Graph polar equations<\/li>\n \t<li>Evaluate the polar form of complex numbers<\/li>\n \t<li>Find parametric equations<\/li>\n \t<li>Graph parametric equations<\/li>\n \t<li>Perform vector operations<\/li>\n<\/ul>\n<h2>Module 11: Analytic Geometry<\/h2>\n<h3>Analyze the graphs and equations of conic sections<\/h3>\n<ul>\n \t<li>Evaluate ellipses<\/li>\n \t<li>Evaluate hyperbolas<\/li>\n \t<li>Evaluate parabolas<\/li>\n \t<li>Evaluate the rotation of axes<\/li>\n \t<li>Evaluate conic sections in polar coordinates<\/li>\n<\/ul>\n<h2>Module 12: Introduction to Calculus<\/h2>\n<h3>Describe how to find limits and derivatives of functions<\/h3>\n<ul>\n \t<li>Find limits using graphs and tables<\/li>\n \t<li>Find limits using properties<\/li>\n \t<li>Determine continuity of functions<\/li>\n \t<li>Find the derivative of a function<\/li>\n<\/ul>\n","rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-254\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2025\/2017\/07\/01225024\/outcomes.jpg\" alt=\"icon of a magnifying glass over a list\" width=\"200\" height=\"201\" \/><\/p>\n<p>The content, assignments, and assessments for Precalculus are aligned to the following learning outcomes. A full list of course learning outcomes can be viewed here: <a href=\"https:\/\/docs.google.com\/spreadsheets\/d\/1YC7umNfGS835ZUHcDM4fixul7fVy-79MxI1aWiTLJno\/edit?usp=sharing\" target=\"_blank\" rel=\"noopener\">Precalculus Learning Outcomes<\/a>.<\/p>\n<h2>Module 1: Introduction to Functions<\/h2>\n<h3>Describe properties of functions and their relationships<\/h3>\n<ul>\n<li>Identify and evaluate functions<\/li>\n<li>Calculate the domain and range of a function<\/li>\n<li>Describe change behaviors of graphs<\/li>\n<li>Evaluate composite functions<\/li>\n<li>Transform functions<\/li>\n<li>Solve absolute value functions<\/li>\n<li>Find inverse functions<\/li>\n<\/ul>\n<h2>Module 2: Linear Functions<\/h2>\n<h3>Understand linear functions, their graphs, and how they relate to data<\/h3>\n<ul>\n<li>Evaluate linear functions<\/li>\n<li>Graph linear functions<\/li>\n<li>Model real world scenarios with linear functions<\/li>\n<li>Use linear models of data to make predictions<\/li>\n<\/ul>\n<h2>Module 3:&nbsp;<span class=\"os-text\">Polynomial and Rational Functions<\/span><\/h2>\n<h3>Evaluate polynomial and rational functions and their graphs<\/h3>\n<ul>\n<li>Simplify complex number expressions<\/li>\n<li>Understand quadratic functions<\/li>\n<li>Identify power functions and polynomial functions<\/li>\n<li>Graph polynomial functions<\/li>\n<li>Divide polynomial functions<\/li>\n<li>Find the zeros of polynomial equations<\/li>\n<li>Graph rational functions<\/li>\n<li>Find inverse functions<\/li>\n<li>Solve direct, indirect, and joint variation problems<\/li>\n<\/ul>\n<h2>Module 4:&nbsp;<span class=\"os-text\">Exponential and Logarithmic Functions<\/span><\/h2>\n<h3>Model growth and decay patterns with exponential and logarithmic functions<\/h3>\n<ul>\n<li>Evaluate exponential functions<\/li>\n<li>Graph exponential functions<\/li>\n<li>Use logarithmic functions<\/li>\n<li>Graph logarithmic functions<\/li>\n<li>Expand and condense logarithmic expressions<\/li>\n<li>Solve exponential and logarithmic equations<\/li>\n<li>Use exponential and logarithmic models<\/li>\n<li>Fit exponential models to data<\/li>\n<\/ul>\n<h2>Module 5: Systems of Equations and Inequalities<\/h2>\n<h3>Evaluate systems of linear and non-linear equations with both two and three variables<\/h3>\n<ul>\n<li>Solve systems of linear equations in two variables<\/li>\n<li>Solve systems of linear equations in three variables<\/li>\n<li>Solve and graph systems of nonlinear equations and inequalities<\/li>\n<li>Decompose partial fractions<\/li>\n<li>Evaluate matrices and matrix operations<\/li>\n<li>Write and solve systems with Gaussian Elimination<\/li>\n<li>Solve systems with inverses<\/li>\n<li>Solve systems with Cramer&#8217;s rule<\/li>\n<\/ul>\n<h2>Module 6: Sequences, Probability, and Counting Theory<\/h2>\n<h3>Solve sequence and counting problems<\/h3>\n<ul>\n<li>Write the terms of a sequence<\/li>\n<li>Evaluate arithmetic sequences<\/li>\n<li>Evaluate geometric sequences<\/li>\n<li>Find the terms of a series<\/li>\n<li>Solve counting problems<\/li>\n<li>Use the binomial theorem<\/li>\n<li>Compute probabilities<\/li>\n<\/ul>\n<h2>Module 7: Trigonometric Functions<\/h2>\n<h3>Evaluate trigonometric functions using angles and right triangles<\/h3>\n<ul>\n<li>Find and use angles<\/li>\n<li>Evaluate sine and cosine functions<\/li>\n<li>Understand other trigonometric functions<\/li>\n<li>Use right triangle trigonometry<\/li>\n<\/ul>\n<h2>Module 8: Periodic Functions<\/h2>\n<h3>Analyze the graphs of trigonometric functions<\/h3>\n<ul>\n<li>Graph sine and cosine functions<\/li>\n<li>Analyze and graph other trigonometric functions<\/li>\n<li>Use inverse trigonometric functions<\/li>\n<\/ul>\n<h2>Module 9: Trigonometric Identities and Equations<\/h2>\n<h3>Solve trigonometric equations using identities<\/h3>\n<ul>\n<li>Solve trigonometric equations with identities<\/li>\n<li>Use sum and difference formulas<\/li>\n<li>Use double-angle, half-angle, and reduction formulas<\/li>\n<li>Use sum-to-product and product-to-sum formulas<\/li>\n<li>Solve trigonometric equations<\/li>\n<li>Model trigonometric equations<\/li>\n<\/ul>\n<h2>Module 10: Further Applications of Trigonometry<\/h2>\n<h3>Apply trigonometric rules to evaluate more complex graphs and equations<\/h3>\n<ul>\n<li>Solve non-right triangles using the Law of Sines<\/li>\n<li>Solve non-right triangles using the Law of Cosines<\/li>\n<li>Identify and use polar coordinates<\/li>\n<li>Graph polar equations<\/li>\n<li>Evaluate the polar form of complex numbers<\/li>\n<li>Find parametric equations<\/li>\n<li>Graph parametric equations<\/li>\n<li>Perform vector operations<\/li>\n<\/ul>\n<h2>Module 11: Analytic Geometry<\/h2>\n<h3>Analyze the graphs and equations of conic sections<\/h3>\n<ul>\n<li>Evaluate ellipses<\/li>\n<li>Evaluate hyperbolas<\/li>\n<li>Evaluate parabolas<\/li>\n<li>Evaluate the rotation of axes<\/li>\n<li>Evaluate conic sections in polar coordinates<\/li>\n<\/ul>\n<h2>Module 12: Introduction to Calculus<\/h2>\n<h3>Describe how to find limits and derivatives of functions<\/h3>\n<ul>\n<li>Find limits using graphs and tables<\/li>\n<li>Find limits using properties<\/li>\n<li>Determine continuity of functions<\/li>\n<li>Find the derivative of a function<\/li>\n<\/ul>\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-1216\">\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>Learning Outcomes. <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>Magnify. <strong>Authored by<\/strong>: Eucalyp. <strong>Provided by<\/strong>: Noun Project. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/thenounproject.com\/term\/magnify\/1276779\/\">https:\/\/thenounproject.com\/term\/magnify\/1276779\/<\/a>. <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":503070,"menu_order":3,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Magnify\",\"author\":\"Eucalyp\",\"organization\":\"Noun Project\",\"url\":\"https:\/\/thenounproject.com\/term\/magnify\/1276779\/\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Learning Outcomes\",\"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-1216","chapter","type-chapter","status-publish","hentry"],"part":1213,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/tulsacc-math1613\/wp-json\/pressbooks\/v2\/chapters\/1216","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/tulsacc-math1613\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/tulsacc-math1613\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/tulsacc-math1613\/wp-json\/wp\/v2\/users\/503070"}],"version-history":[{"count":0,"href":"https:\/\/courses.lumenlearning.com\/tulsacc-math1613\/wp-json\/pressbooks\/v2\/chapters\/1216\/revisions"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/tulsacc-math1613\/wp-json\/pressbooks\/v2\/parts\/1213"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/tulsacc-math1613\/wp-json\/pressbooks\/v2\/chapters\/1216\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/tulsacc-math1613\/wp-json\/wp\/v2\/media?parent=1216"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/tulsacc-math1613\/wp-json\/pressbooks\/v2\/chapter-type?post=1216"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/tulsacc-math1613\/wp-json\/wp\/v2\/contributor?post=1216"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/tulsacc-math1613\/wp-json\/wp\/v2\/license?post=1216"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}