{"id":4584,"date":"2017-12-20T19:08:28","date_gmt":"2017-12-20T19:08:28","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/waymakerintermediatealgebra\/?post_type=chapter&#038;p=4584"},"modified":"2021-06-11T17:23:48","modified_gmt":"2021-06-11T17:23:48","slug":"learning-outcomes","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/chapter\/learning-outcomes\/","title":{"raw":"Learning Outcomes","rendered":"Learning Outcomes"},"content":{"raw":"<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\" \/>\r\n\r\nThe content, assignments, and assessments for Intermediate Algebra 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\/11iOHFPzSgK2_x7eUxk8INBwy8p6-1K-qtTWQNGcbYpc\/edit?usp=sharing\" target=\"_blank\" rel=\"noopener\">Intermediate Algebra Learning Outcomes.<\/a>\r\n<h2>Module 0: Review<\/h2>\r\n<ul>\r\n \t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Use the Order of Operations&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:23427,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;,&quot;17&quot;:1}\">Use the Order of Operations<\/span><\/li>\r\n \t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Arithmetic With Fractions&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:23427,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;,&quot;17&quot;:1}\">Arithmetic With Fractions<\/span><\/li>\r\n<\/ul>\r\n<h2>Module 1: Real Numbers and Algebraic Expressions<\/h2>\r\n<ul>\r\n \t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Classify and Define Properties of Real Numbers&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:23427,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;,&quot;17&quot;:1}\">Classify and Define Properties of Real Numbers<\/span><\/li>\r\n \t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Solve Multi-Step Linear Equations&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:23427,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;,&quot;17&quot;:1}\">Solve Multi-Step Linear Equations<\/span><\/li>\r\n \t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Problem Solving&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:23427,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;,&quot;17&quot;:1}\">Problem Solving<\/span><\/li>\r\n<\/ul>\r\n<h2>Module 2: Linear Inequalities<\/h2>\r\n<ul>\r\n \t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Solve Single- and Multi-Step Inequalities&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:23427,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;,&quot;17&quot;:1}\">Solve Single- and Multi-Step Inequalities<\/span><\/li>\r\n \t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Solve Compound Inequalities&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:23427,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;,&quot;17&quot;:1}\">Solve Compound Inequalities<\/span><\/li>\r\n<\/ul>\r\n<h2>Module 3: Graph Linear Equations and Inequalities<\/h2>\r\n<ul>\r\n \t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Graph Linear Equations in Two Variables&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Graph Linear Equations in Two Variables<\/span><\/li>\r\n \t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Graph Linear Inequalities&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Graph Linear Inequalities<\/span><\/li>\r\n<\/ul>\r\n<h2>Module 4: Functions and Function Notation<\/h2>\r\n<ul>\r\n \t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Functions and Their Notation&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Functions and Their Notation<\/span><\/li>\r\n \t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Graphs of Functions&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Graphs of Functions<\/span><\/li>\r\n \t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Domain and Range&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Domain and Range<\/span><\/li>\r\n<\/ul>\r\n<h2>Module 5: Linear Functions<\/h2>\r\n<ul>\r\n \t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Characteristics of Linear Functions and Their Graphs&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Characteristics of Linear Functions and Their Graphs<\/span><\/li>\r\n \t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Equations of Linear Functions&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Equations of Linear Functions<\/span><\/li>\r\n \t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Piecewise-Defined Linear Functions&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Piecewise-Defined Linear Functions<\/span><\/li>\r\n<\/ul>\r\n<h2>Module 6: Linear Systems<\/h2>\r\n<ul>\r\n \t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Solve Systems in Two Variables&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Solve Systems in Two Variables<\/span><\/li>\r\n \t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Systems of Equations in Three Variables&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Systems of Equations in Three Variables<\/span><\/li>\r\n \t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Systems of Linear Inequalities&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Systems of Linear Inequalities<\/span><\/li>\r\n<\/ul>\r\n<h2>Module 7: Exponents<\/h2>\r\n<ul>\r\n \t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Apply Exponent Rules&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Apply Exponent Rules<\/span><\/li>\r\n \t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Scientific Notation&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Scientific Notation<\/span><\/li>\r\n<\/ul>\r\n<h2>Module 8: Polynomials and Polynomial Functions<\/h2>\r\n<ul>\r\n \t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Algebraic Operations on Polynomials&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Algebraic Operations on Polynomials<\/span><\/li>\r\n \t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Polynomial Functions&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Polynomial Functions<\/span><\/li>\r\n<\/ul>\r\n<h2>Module 9: Factoring<\/h2>\r\n<ul>\r\n \t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Factor Trinomials&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Factor Trinomials<\/span><\/li>\r\n \t<li>Special Cases<\/li>\r\n \t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Polynomial Equations&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Polynomial Equations<\/span><\/li>\r\n<\/ul>\r\n<h2>Module 10: Rational Expressions and Equations<\/h2>\r\n<ul>\r\n \t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Operations With Rational Expressions&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Operations With Rational Expressions<\/span><\/li>\r\n \t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Rational Equations and Their Applications&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Rational Equations and Their Applications<\/span><\/li>\r\n<\/ul>\r\n<h2>Module 11: Roots and Rational Exponents<\/h2>\r\n<ul>\r\n \t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Simplify Roots and Rational Exponents&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Simplify Roots and Rational Exponents<\/span><\/li>\r\n \t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Algebraic Operations with Radical Expressions&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Algebraic Operations with Radical Expressions<\/span><\/li>\r\n \t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Equations with Radicals&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Equations with Radicals<\/span><\/li>\r\n<\/ul>\r\n<h2>Module 12: Quadratic Equations and Complex Numbers<\/h2>\r\n<ul>\r\n \t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Quadratic Equations&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Quadratic Equations<\/span><\/li>\r\n \t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Complex Numbers&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Complex Numbers<\/span><\/li>\r\n \t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Quadratic Equations with Complex Solutions&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Quadratic Equations with Complex Solutions<\/span><\/li>\r\n<\/ul>\r\n<h2>Module 13: Exponential, and Logarithmic Functions<\/h2>\r\n<ul>\r\n \t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Exponential Functions&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Exponential Functions<\/span><\/li>\r\n \t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Logarithmic Functions&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Logarithmic Functions<\/span><\/li>\r\n<\/ul>\r\n<h2>Module 14: Exponential and Logarithmic Equations<\/h2>\r\n<ul>\r\n \t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Logarithmic Properties&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Logarithmic Properties<\/span><\/li>\r\n \t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Exponential and Logarithmic Equations&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Exponential and Logarithmic Equations<\/span><\/li>\r\n<\/ul>","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 Intermediate Algebra 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\/11iOHFPzSgK2_x7eUxk8INBwy8p6-1K-qtTWQNGcbYpc\/edit?usp=sharing\" target=\"_blank\" rel=\"noopener\">Intermediate Algebra Learning Outcomes.<\/a><\/p>\n<h2>Module 0: Review<\/h2>\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Use the Order of Operations&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:23427,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;,&quot;17&quot;:1}\">Use the Order of Operations<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Arithmetic With Fractions&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:23427,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;,&quot;17&quot;:1}\">Arithmetic With Fractions<\/span><\/li>\n<\/ul>\n<h2>Module 1: Real Numbers and Algebraic Expressions<\/h2>\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Classify and Define Properties of Real Numbers&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:23427,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;,&quot;17&quot;:1}\">Classify and Define Properties of Real Numbers<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Solve Multi-Step Linear Equations&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:23427,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;,&quot;17&quot;:1}\">Solve Multi-Step Linear Equations<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Problem Solving&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:23427,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;,&quot;17&quot;:1}\">Problem Solving<\/span><\/li>\n<\/ul>\n<h2>Module 2: Linear Inequalities<\/h2>\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Solve Single- and Multi-Step Inequalities&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:23427,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;,&quot;17&quot;:1}\">Solve Single- and Multi-Step Inequalities<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Solve Compound Inequalities&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:23427,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;,&quot;17&quot;:1}\">Solve Compound Inequalities<\/span><\/li>\n<\/ul>\n<h2>Module 3: Graph Linear Equations and Inequalities<\/h2>\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Graph Linear Equations in Two Variables&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Graph Linear Equations in Two Variables<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Graph Linear Inequalities&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Graph Linear Inequalities<\/span><\/li>\n<\/ul>\n<h2>Module 4: Functions and Function Notation<\/h2>\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Functions and Their Notation&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Functions and Their Notation<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Graphs of Functions&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Graphs of Functions<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Domain and Range&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Domain and Range<\/span><\/li>\n<\/ul>\n<h2>Module 5: Linear Functions<\/h2>\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Characteristics of Linear Functions and Their Graphs&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Characteristics of Linear Functions and Their Graphs<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Equations of Linear Functions&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Equations of Linear Functions<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Piecewise-Defined Linear Functions&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Piecewise-Defined Linear Functions<\/span><\/li>\n<\/ul>\n<h2>Module 6: Linear Systems<\/h2>\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Solve Systems in Two Variables&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Solve Systems in Two Variables<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Systems of Equations in Three Variables&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Systems of Equations in Three Variables<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Systems of Linear Inequalities&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Systems of Linear Inequalities<\/span><\/li>\n<\/ul>\n<h2>Module 7: Exponents<\/h2>\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Apply Exponent Rules&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Apply Exponent Rules<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Scientific Notation&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Scientific Notation<\/span><\/li>\n<\/ul>\n<h2>Module 8: Polynomials and Polynomial Functions<\/h2>\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Algebraic Operations on Polynomials&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Algebraic Operations on Polynomials<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Polynomial Functions&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Polynomial Functions<\/span><\/li>\n<\/ul>\n<h2>Module 9: Factoring<\/h2>\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Factor Trinomials&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Factor Trinomials<\/span><\/li>\n<li>Special Cases<\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Polynomial Equations&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Polynomial Equations<\/span><\/li>\n<\/ul>\n<h2>Module 10: Rational Expressions and Equations<\/h2>\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Operations With Rational Expressions&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Operations With Rational Expressions<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Rational Equations and Their Applications&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Rational Equations and Their Applications<\/span><\/li>\n<\/ul>\n<h2>Module 11: Roots and Rational Exponents<\/h2>\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Simplify Roots and Rational Exponents&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Simplify Roots and Rational Exponents<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Algebraic Operations with Radical Expressions&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Algebraic Operations with Radical Expressions<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Equations with Radicals&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Equations with Radicals<\/span><\/li>\n<\/ul>\n<h2>Module 12: Quadratic Equations and Complex Numbers<\/h2>\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Quadratic Equations&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Quadratic Equations<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Complex Numbers&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Complex Numbers<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Quadratic Equations with Complex Solutions&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Quadratic Equations with Complex Solutions<\/span><\/li>\n<\/ul>\n<h2>Module 13: Exponential, and Logarithmic Functions<\/h2>\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Exponential Functions&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Exponential Functions<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Logarithmic Functions&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Logarithmic Functions<\/span><\/li>\n<\/ul>\n<h2>Module 14: Exponential and Logarithmic Equations<\/h2>\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Logarithmic Properties&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Logarithmic Properties<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Exponential and Logarithmic Equations&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7043,&quot;3&quot;:[null,0],&quot;4&quot;:[null,2,12507122],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:[null,2,0],&quot;15&quot;:&quot;Calibri&quot;}\">Exponential and Logarithmic Equations<\/span><\/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-4584\">\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":26254,"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-4584","chapter","type-chapter","status-web-only","hentry"],"part":4575,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters\/4584","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/wp\/v2\/users\/26254"}],"version-history":[{"count":12,"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters\/4584\/revisions"}],"predecessor-version":[{"id":5675,"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters\/4584\/revisions\/5675"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/pressbooks\/v2\/parts\/4575"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters\/4584\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/wp\/v2\/media?parent=4584"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=4584"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/wp\/v2\/contributor?post=4584"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/wp\/v2\/license?post=4584"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}