{"id":4340,"date":"2017-06-02T21:09:20","date_gmt":"2017-06-02T21:09:20","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/waymakercollegealgebra\/?post_type=front-matter&#038;p=4340"},"modified":"2017-06-02T21:09:20","modified_gmt":"2017-06-02T21:09:20","slug":"course-learning-outcomes","status":"publish","type":"front-matter","link":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/front-matter\/course-learning-outcomes\/","title":{"raw":"Course Learning Outcomes","rendered":"Course Learning Outcomes"},"content":{"raw":"<h2>Module 1: Algebra Essentials<\/h2>\r\n<h3>Real Numbers<\/h3>\r\n<ul>\r\n \t<li>Classify a real number<\/li>\r\n \t<li>Perform calculations using order of operations.<\/li>\r\n \t<li>Use the properties of real numbers<\/li>\r\n \t<li>Evaluate and simplify algebraic expressions.<\/li>\r\n<\/ul>\r\n<h3>Exponents and Scientific Notation<\/h3>\r\n<ul>\r\n \t<li>Use the rules of exponents to simplify exponential expressions<\/li>\r\n \t<li>Use scientific notation<\/li>\r\n<\/ul>\r\n<h3>Radicals and Rational Exponents<\/h3>\r\n<ul>\r\n \t<li>Evaluate and simplify square roots<\/li>\r\n \t<li>Rationalize a denominator that contains a square root<\/li>\r\n \t<li>Rewrite a radical expression using rational exponents<\/li>\r\n<\/ul>\r\n<h2>Module 2: Polynomial and Rational Expressions<\/h2>\r\n<h3>Polynomial Basics<\/h3>\r\n<ul>\r\n \t<li>Identify the degree, leading coefficient, and leading term of a polynomial expression<\/li>\r\n \t<li>Perform algebraic operations on polynomial expressions<\/li>\r\n<\/ul>\r\n<h3>Factoring Polynomials<\/h3>\r\n<ul>\r\n \t<li>Identify the greatest common factor of a polynomial expression<\/li>\r\n \t<li>Factor a wide variety of polynomials including those with fractional or negative exponents<\/li>\r\n<\/ul>\r\n<h3>Rational Expressions<\/h3>\r\n<ul>\r\n \t<li>Simplify and perform algebraic operations on rational expressions<\/li>\r\n<\/ul>\r\n<h2>Module 3: The Rectangular Coordinate System and Equations of Lines<\/h2>\r\n<h3>Points and Lines in the Plane<\/h3>\r\n<ul>\r\n \t<li>Plot ordered pairs, and graph equations by plotting points<\/li>\r\n \t<li>Use a graphing utility to graph equations<\/li>\r\n \t<li>Find the x and y intercepts of a graphed equation<\/li>\r\n \t<li>Use the distance and midpoint formulas<\/li>\r\n<\/ul>\r\n<h3>Equations of Lines<\/h3>\r\n<ul>\r\n \t<li>Write equations of lines in slope-intercept, point-slope, and standard forms<\/li>\r\n \t<li>Identify the equations and graphs of horizontal and vertical lines<\/li>\r\n \t<li>Determine whether two lines are parallel, perpendicular, or neither<\/li>\r\n \t<li>Write equations of lines that are parallel or perpendicular to another line<\/li>\r\n<\/ul>\r\n<h3>Models and Applications of Linear Equations<\/h3>\r\n<ul>\r\n \t<li>Develop a problem solving method<\/li>\r\n \t<li>Write an equation to model an application<\/li>\r\n \t<li>Solve distance, rate and time problems<\/li>\r\n \t<li>Solve perimeter, area, and volume problems<\/li>\r\n<\/ul>\r\n<h2>Module 4: Equations and Inequalities<\/h2>\r\n<h3>Equation-Solving Techniques<\/h3>\r\n<ul>\r\n \t<li>Solve equations involving rational exponents.<\/li>\r\n \t<li>Solve equations using factoring.<\/li>\r\n \t<li>Solve radical equations.<\/li>\r\n \t<li>Solve absolute value equations<\/li>\r\n<\/ul>\r\n<h3>Models and Applications<\/h3>\r\n<ul>\r\n \t<li>Set up a linear equation to solve a real-world application.<\/li>\r\n \t<li>Use a formula to solve a real-world application.<\/li>\r\n<\/ul>\r\n<h3>Quadratic Equations<\/h3>\r\n<ul>\r\n \t<li>Solve quadratic equations by factoring.<\/li>\r\n \t<li>Solve quadratic equations by the square root property.<\/li>\r\n \t<li>Solve quadratic equations by completing the square.<\/li>\r\n \t<li>Solve quadratic equations by using the quadratic formula.<\/li>\r\n<\/ul>\r\n<h3>Linear Inequalities and Absolute Value Inequalities<\/h3>\r\n<ul>\r\n \t<li>Use interval notation.<\/li>\r\n \t<li>Use properties of inequalities.<\/li>\r\n \t<li>Solve inequalities in one variable algebraically.<\/li>\r\n \t<li>Solve absolute value inequalities<\/li>\r\n<\/ul>\r\n<h2>Module 5: Function Basics<\/h2>\r\n<h3>Characteristics of Functions and Their Graphs<\/h3>\r\n<ul>\r\n \t<li>Determine whether a relation represents a function.<\/li>\r\n \t<li>Find the value of a function.<\/li>\r\n \t<li>Determine whether a function is one-to-one.<\/li>\r\n \t<li>Use the vertical line test to identify functions.<\/li>\r\n \t<li>Graph the functions listed in the library of functions<\/li>\r\n<\/ul>\r\n<h3>Domain and Range of Functions<\/h3>\r\n<ul>\r\n \t<li>Find the domain of a function defined by an equation<\/li>\r\n \t<li>Write Domain and Range Using Standard Notations<\/li>\r\n \t<li>Find Domain and Range from a Graph<\/li>\r\n \t<li>Define Domain and Range of Toolkit Functions<\/li>\r\n \t<li>Graph Piecewise-Defined Functions<\/li>\r\n<\/ul>\r\n<h3>Rates of Change and Behavior of Graphs<\/h3>\r\n<ul>\r\n \t<li>Find the average rate of change of a function.<\/li>\r\n \t<li>Use a graph to determine where a function is increasing, decreasing, or constant.<\/li>\r\n \t<li>Use a graph to locate local maxima and local minima.<\/li>\r\n \t<li>Use a graph to locate the absolute maximum and absolute minimum.<\/li>\r\n<\/ul>\r\n<h2>Module 6:\u00a0Algebraic Operations on Functions<\/h2>\r\n<h3>Compositions of Functions<\/h3>\r\n<ul>\r\n \t<li>Combine functions using algebraic operations.<\/li>\r\n \t<li>Create a new function by composition of functions.<\/li>\r\n \t<li>Evaluate composite functions.<\/li>\r\n \t<li>Find the domain of a composite function.<\/li>\r\n \t<li>Decompose a composite function into its component functions.<\/li>\r\n<\/ul>\r\n<h3>Transformations of Functions<\/h3>\r\n<ul>\r\n \t<li>Graph functions using vertical and horizontal shifts.<\/li>\r\n \t<li>Graph functions using reflections about the [latex]x[\/latex] -axis and the [latex]y[\/latex] -axis.<\/li>\r\n \t<li>Determine whether a function is even, odd, or neither from its graph.<\/li>\r\n \t<li>Graph functions using compressions and stretches.<\/li>\r\n \t<li>Combine transformations.<\/li>\r\n<\/ul>\r\n<h3>Inverse Functions<\/h3>\r\n<ul>\r\n \t<li>Verify inverse functions.<\/li>\r\n \t<li>Determine the domain and range of an inverse function, and restrict the domain of a function to make it one-to-one.<\/li>\r\n \t<li>Find or evaluate the inverse of a function.<\/li>\r\n \t<li>Use the graph of a one-to-one function to graph its inverse function on the same axes.<\/li>\r\n<\/ul>\r\n<h2>Module 7: Linear and Absolute Value Functions<\/h2>\r\n<h3>Linear Functions<\/h3>\r\n<ul>\r\n \t<li>Represent a linear function with an equation, words, a table and a graph<\/li>\r\n \t<li>Determine whether a linear function is increasing, decreasing, or constant.<\/li>\r\n \t<li>Write and interpret a linear function.<\/li>\r\n<\/ul>\r\n<h3>Graphs of Linear Functions<\/h3>\r\n<ul>\r\n \t<li>Graph linear functions by plotting points, using the slope and y-intercept, and by using transformations<\/li>\r\n \t<li>Write the equation of a linear function given it's graph, including vertical and horizontal lines, match linear equations with their graphs<\/li>\r\n \t<li>Find the equations of vertical and horizontal lines<\/li>\r\n \t<li>Graph an absolute value function, find it's intercepts<\/li>\r\n<\/ul>\r\n<h3>Modeling With Linear Functions<\/h3>\r\n<ul>\r\n \t<li>Identify steps for modeling and solving.<\/li>\r\n \t<li>Build linear models from verbal descriptions.<\/li>\r\n \t<li>Draw and interpret scatter plots.<\/li>\r\n \t<li>Find the line of best fit using the Desmos calculator.<\/li>\r\n \t<li>Distinguish between linear and nonlinear relations.<\/li>\r\n \t<li>Use a linear model to make predictions.<\/li>\r\n<\/ul>\r\n<h2>Module 8:\u00a0Quadratic Functions<\/h2>\r\n<h3>Complex Numbers<\/h3>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\">Express square roots of negative numbers as multiples of\u2009i<\/li>\r\n \t<li style=\"font-weight: 400;\">Plot complex numbers on the complex plane<\/li>\r\n \t<li style=\"font-weight: 400;\">Add and subtract complex numbers<\/li>\r\n \t<li style=\"font-weight: 400;\">Multiply and divide complex numbers<\/li>\r\n<\/ul>\r\n<h3>Graphs of Quadratic Functions<\/h3>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\">Recognize characteristics of parabolas<\/li>\r\n \t<li style=\"font-weight: 400;\">Understand how the graph of a parabola is related to its quadratic function<\/li>\r\n<\/ul>\r\n<h3>Analysis of Quadratic Functions<\/h3>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\">Use the quadratic formula and factoring to find both real and complex roots (x-intercepts) of quadratic functions<\/li>\r\n \t<li style=\"font-weight: 400;\">Use algebra to find the y-intercepts of a quadratic function<\/li>\r\n \t<li style=\"font-weight: 400;\">Solve problems involving the roots and intercepts of a quadratic function<\/li>\r\n \t<li style=\"font-weight: 400;\">Use the discriminant to determine the nature (real or complex) and quantity of solutions to quadratic equations<\/li>\r\n \t<li style=\"font-weight: 400;\">Determine a quadratic function\u2019s minimum or maximum value<\/li>\r\n \t<li style=\"font-weight: 400;\">Solve problems involving a quadratic function\u2019s minimum or maximum value<\/li>\r\n<\/ul>\r\n<h2>Module 9: Power and Polynomial Functions<\/h2>\r\n<h3>Characteristics of Power and Polynomial Functions<\/h3>\r\n<ul>\r\n \t<li>Identify power functions.<\/li>\r\n \t<li>Identify end behavior of power functions.<\/li>\r\n \t<li>Identify polynomial functions.<\/li>\r\n \t<li>Identify the degree and leading coefficient of polynomial functions.<\/li>\r\n \t<li>Identify local behavior of polynomial functions.<\/li>\r\n<\/ul>\r\n<h3>Graphs of Polynomial Functions<\/h3>\r\n<ul>\r\n \t<li>Identify zeros of polynomial functions with even and odd multiplicity<\/li>\r\n \t<li>Use the degree of a polynomial\u00a0to determine the number of turning points of its graph<\/li>\r\n \t<li>Draw the graph of a polynomial function using end behavior, turning points, intercepts, and the intermediate value theorem<\/li>\r\n \t<li>Write the equation of a polynomial function given it's graph<\/li>\r\n<\/ul>\r\n<h3>Divide Polynomials<\/h3>\r\n<ul>\r\n \t<li>Use long division to divide polynomials.<\/li>\r\n \t<li>Use synthetic division to divide polynomials.<\/li>\r\n<\/ul>\r\n<h3>Methods for Finding Zeros of Polynomials<\/h3>\r\n<ul>\r\n \t<li>Evaluate a polynomial using the Remainder Theorem.<\/li>\r\n \t<li>Use the Factor Theorem to solve a polynomial equation.<\/li>\r\n \t<li>Use the Rational Zero Theorem to find rational zeros.<\/li>\r\n \t<li>Find zeros of a polynomial function.<\/li>\r\n \t<li>Use the Linear Factorization Theorem to find polynomials with given zeros.<\/li>\r\n \t<li>Use Descartes\u2019 Rule of Signs.<\/li>\r\n \t<li>Solve real-world applications of polynomial equations<\/li>\r\n<\/ul>\r\n<h2>Module 10: Rational and Radical Functions<\/h2>\r\n<h3>Rational Functions<\/h3>\r\n<ul>\r\n \t<li>Use arrow notation to describe end behavior of rational functions<\/li>\r\n \t<li>Solve applied problems involving rational functions.<\/li>\r\n \t<li>Find the domains of rational functions.<\/li>\r\n \t<li>Identify vertical and horizontal asymptotes of graphs of rational functions<\/li>\r\n \t<li>Graph rational functions.<\/li>\r\n<\/ul>\r\n<h3>Radical Functions<\/h3>\r\n<ul>\r\n \t<li>Find the inverse of a polynomial function.<\/li>\r\n \t<li>Restrict the domain to find the inverse of a polynomial function.<\/li>\r\n<\/ul>\r\n<h3>Variation<\/h3>\r\n<ul>\r\n \t<li>Solve direct variation problems.<\/li>\r\n \t<li>Solve inverse variation problems.<\/li>\r\n \t<li>Solve problems involving joint variation.<\/li>\r\n<\/ul>\r\n<h2>Module 11:\u00a0Exponential and Logarithmic Functions<\/h2>\r\n<h3>Exponential Functions<\/h3>\r\n<ul>\r\n \t<li>Evaluate an exponential growth function with different bases<\/li>\r\n \t<li>Use a compound interest Formula<\/li>\r\n \t<li>Write an exponential function<\/li>\r\n \t<li>Find an exponential function given a graph<\/li>\r\n \t<li>Use a graphing calculator to find an exponential function<\/li>\r\n \t<li>Find an exponential function that models continuous growth or decay<\/li>\r\n<\/ul>\r\n<h3>Graphs of Exponential Functions<\/h3>\r\n<ul>\r\n \t<li>Graph exponential functions, determine whether a graph represents exponential growth or decay<\/li>\r\n \t<li>Graph exponential functions using transformations.<\/li>\r\n<\/ul>\r\n<h3>Logarithmic Functions<\/h3>\r\n<ul>\r\n \t<li>Convert from logarithmic to exponential form.<\/li>\r\n \t<li>Convert from exponential to logarithmic form.<\/li>\r\n \t<li>Evaluate common and natural logarithms.<\/li>\r\n<\/ul>\r\n<h3>Graphs of Logarithmic Functions<\/h3>\r\n<ul>\r\n \t<li>Identify the domain of a logarithmic function.<\/li>\r\n \t<li>Graph logarithmic functions using transformations, and identify intercepts and the vertical asymptote<\/li>\r\n \t<li>Identify why and how a logarithmic function is an inverse of an exponential function<\/li>\r\n<\/ul>\r\n<h2>Module 12:\u00a0Exponential and Logarithmic Equations and Models<\/h2>\r\n<h3>Logarithmic Properties<\/h3>\r\n<ul>\r\n \t<li>Use power, product, and quotient rules to expand and condense logarithms<\/li>\r\n \t<li>Use the change-of-base formula for logarithms.<\/li>\r\n<\/ul>\r\n<h3>Exponential and Logarithmic Equations<\/h3>\r\n<ul>\r\n \t<li>Use like bases to solve exponential equations.<\/li>\r\n \t<li>Use logarithms to solve exponential equations.<\/li>\r\n \t<li>Use the definition of a logarithm to solve logarithmic equations.<\/li>\r\n \t<li>Use the one-to-one property of logarithms to solve logarithmic equations.<\/li>\r\n \t<li>Solve applied problems involving exponential and logarithmic equations.<\/li>\r\n<\/ul>\r\n<h3>Exponential and Logarithmic Models<\/h3>\r\n<ul>\r\n \t<li>Model exponential growth and decay.<\/li>\r\n \t<li>Use Newton\u2019s Law of Cooling.<\/li>\r\n \t<li>Use logistic-growth models.<\/li>\r\n \t<li>Choose an appropriate model for data.<\/li>\r\n \t<li>Express an exponential model in base <em>e<\/em>.<\/li>\r\n<\/ul>\r\n<h3>Fitting Exponential Models to Data<\/h3>\r\n<ul>\r\n \t<li>Build an exponential model from data.<\/li>\r\n \t<li>Build a logarithmic model from data.<\/li>\r\n \t<li>Build a logistic model from data.<\/li>\r\n<\/ul>\r\n<h2>Module 13:\u00a0Systems of Equations and Inequalities<\/h2>\r\n<h3>Systems of Linear Equations: Two Variables<\/h3>\r\n<ul>\r\n \t<li>Solve systems of equations by graphing,\u00a0substitution, and\u00a0addition.<\/li>\r\n \t<li>Identify inconsistent systems of equations containing two variables.<\/li>\r\n \t<li>Express the solution of a system of dependent equations containing two variables using standard notations.<\/li>\r\n<\/ul>\r\n<h3>Systems of Nonlinear Equations and Inequalities<\/h3>\r\n<ul>\r\n \t<li>Solve a system of nonlinear equations using substitution or elimination.<\/li>\r\n \t<li>Graph a nonlinear inequality.<\/li>\r\n \t<li>Graph a system of nonlinear inequalities.<\/li>\r\n<\/ul>\r\n<h3>Systems of Linear Equations: Three Variables<\/h3>\r\n<ul>\r\n \t<li>Solve systems of three equations in three variables.<\/li>\r\n \t<li>Identify inconsistent systems of equations containing three variables.<\/li>\r\n \t<li>Express the solution of a system of dependent equations containing three variables using standard notations.<\/li>\r\n<\/ul>\r\n<h3>Partial Fractions: an Application of Systems<\/h3>\r\n<ul>\r\n \t<li>Decompose \u2009 [latex]\\frac{{P( x )}}{{ Q( x )}}[\/latex] ,\u2009 where \u2009Q( x )\u2009 has only nonrepeated linear factors.<\/li>\r\n \t<li>Decompose \u2009[latex]\\frac{{P( x )}}{{ Q( x )}}[\/latex] ,\u2009 where \u2009Q( x )\u2009 has repeated linear factors.<\/li>\r\n \t<li>Decompose \u2009[latex]\\frac{{P( x )}}{{ Q( x )}}[\/latex] ,\u2009 where \u2009Q( x )\u2009 has a nonrepeated irreducible quadratic factor.<\/li>\r\n \t<li>Decompose \u2009[latex]\\frac{{P( x )}}{{ Q( x )}}[\/latex] ,\u2009 where \u2009Q( x )\u2009 has a repeated irreducible quadratic factor.<\/li>\r\n<\/ul>\r\n<h2>Module 14: Solve Systems With Matrices<\/h2>\r\n<h3>Matrices and Matrix Operations<\/h3>\r\n<ul>\r\n \t<li>Find the sum and difference of two matrices.<\/li>\r\n \t<li>Find scalar multiples of a matrix.<\/li>\r\n \t<li>Find the product of two matrices.<\/li>\r\n<\/ul>\r\n<h3>Gaussian Elimination<\/h3>\r\n<ul>\r\n \t<li>Write the augmented matrix of a system of equations.<\/li>\r\n \t<li>Write the system of equations from an augmented matrix.<\/li>\r\n \t<li>Perform row operations on a matrix.<\/li>\r\n \t<li>Solve a system of linear equations using matrices.<\/li>\r\n<\/ul>\r\n<h3>Solve Systems with Inverses<\/h3>\r\n<ul>\r\n \t<li>Find the inverse of a matrix.<\/li>\r\n \t<li>Solve a system of linear equations using an inverse matrix.<\/li>\r\n<\/ul>\r\n<h2>Module 15: Conic Sections<\/h2>\r\n<h3>The Ellipse<\/h3>\r\n<ul>\r\n \t<li>Write equations of ellipses in standard form.<\/li>\r\n \t<li>Graph ellipses centered at the origin.<\/li>\r\n \t<li>Graph ellipses not centered at the origin.<\/li>\r\n \t<li>Solve applied problems involving ellipses.<\/li>\r\n<\/ul>\r\n<h3>The Hyperbola<\/h3>\r\n<ul>\r\n \t<li>Locate a hyperbola\u2019s vertices and foci.<\/li>\r\n \t<li>Write equations of hyperbolas in standard form.<\/li>\r\n \t<li>Graph hyperbolas centered at the origin.<\/li>\r\n \t<li>Graph hyperbolas not centered at the origin.<\/li>\r\n \t<li>Solve applied problems involving hyperbolas.<\/li>\r\n<\/ul>\r\n<h3>The Parabola<\/h3>\r\n<ul>\r\n \t<li>Graph parabolas with vertices at the origin.<\/li>\r\n \t<li>Write equations of parabolas in standard form.<\/li>\r\n \t<li>Graph parabolas with vertices not at the origin.<\/li>\r\n \t<li>Solve applied problems involving parabolas.<\/li>\r\n<\/ul>\r\n<h2>Module 16:\u00a0Sequences and Series<\/h2>\r\n<h3>Sequences and Their Notations<\/h3>\r\n<ul>\r\n \t<li>Write the terms of a sequence defined by an explicit formula.<\/li>\r\n \t<li>Write the terms of a sequence defined by a recursive formula.<\/li>\r\n \t<li>Use factorial notation.<\/li>\r\n<\/ul>\r\n<h3>\u00a0Arithmetic Sequences<\/h3>\r\n<ul>\r\n \t<li>Find the common difference for an arithmetic sequence.<\/li>\r\n \t<li>Write terms of an arithmetic sequence.<\/li>\r\n \t<li>Use a recursive formula for an arithmetic sequence.<\/li>\r\n \t<li>Use an explicit formula for an arithmetic sequence.<\/li>\r\n<\/ul>\r\n<h3>Geometric Sequences<\/h3>\r\n<ul>\r\n \t<li>Find the common ratio for a geometric sequence.<\/li>\r\n \t<li>List the terms of a geometric sequence.<\/li>\r\n \t<li>Use a recursive formula for a geometric sequence.<\/li>\r\n \t<li>Use an explicit formula for a geometric sequence.<\/li>\r\n<\/ul>\r\n<h3>Series and Their Notations<\/h3>\r\n<ul>\r\n \t<li>Use summation notation.<\/li>\r\n \t<li>Use the formula for the sum of the \ufb01rst [latex]n[\/latex] terms of an arithmetic series.<\/li>\r\n \t<li>Use the formula for the sum of the \ufb01rst [latex]n[\/latex] terms of a geometric series.<\/li>\r\n \t<li>Use the formula for the sum of an in\ufb01nite geometric series.<\/li>\r\n \t<li>Solve annuity problems.<\/li>\r\n<\/ul>\r\n<h2>Module 17: Counting Principles<\/h2>\r\n<h3>Counting Principles<\/h3>\r\n<ul>\r\n \t<li>Solve counting problems using the Addition Principle and the\u00a0Multiplication Principle.<\/li>\r\n \t<li>Solve counting problems using permutations and combinations \u00a0involving n distinct objects.<\/li>\r\n \t<li>Find the number of subsets of a given set.<\/li>\r\n \t<li>Solve counting problems using permutations involving n non-distinct objects.<\/li>\r\n \t<li>Apply the Binomial Theorem<\/li>\r\n<\/ul>\r\n<h3>Probability<\/h3>\r\n<ul>\r\n \t<li>Construct probability models.<\/li>\r\n \t<li>Compute probabilities of equally likely outcomes.<\/li>\r\n \t<li>Compute probabilities of the union of two events.<\/li>\r\n \t<li>Use the complement rule to find probabilities.<\/li>\r\n \t<li>Compute probability using counting theory.<\/li>\r\n<\/ul>","rendered":"<h2>Module 1: Algebra Essentials<\/h2>\n<h3>Real Numbers<\/h3>\n<ul>\n<li>Classify a real number<\/li>\n<li>Perform calculations using order of operations.<\/li>\n<li>Use the properties of real numbers<\/li>\n<li>Evaluate and simplify algebraic expressions.<\/li>\n<\/ul>\n<h3>Exponents and Scientific Notation<\/h3>\n<ul>\n<li>Use the rules of exponents to simplify exponential expressions<\/li>\n<li>Use scientific notation<\/li>\n<\/ul>\n<h3>Radicals and Rational Exponents<\/h3>\n<ul>\n<li>Evaluate and simplify square roots<\/li>\n<li>Rationalize a denominator that contains a square root<\/li>\n<li>Rewrite a radical expression using rational exponents<\/li>\n<\/ul>\n<h2>Module 2: Polynomial and Rational Expressions<\/h2>\n<h3>Polynomial Basics<\/h3>\n<ul>\n<li>Identify the degree, leading coefficient, and leading term of a polynomial expression<\/li>\n<li>Perform algebraic operations on polynomial expressions<\/li>\n<\/ul>\n<h3>Factoring Polynomials<\/h3>\n<ul>\n<li>Identify the greatest common factor of a polynomial expression<\/li>\n<li>Factor a wide variety of polynomials including those with fractional or negative exponents<\/li>\n<\/ul>\n<h3>Rational Expressions<\/h3>\n<ul>\n<li>Simplify and perform algebraic operations on rational expressions<\/li>\n<\/ul>\n<h2>Module 3: The Rectangular Coordinate System and Equations of Lines<\/h2>\n<h3>Points and Lines in the Plane<\/h3>\n<ul>\n<li>Plot ordered pairs, and graph equations by plotting points<\/li>\n<li>Use a graphing utility to graph equations<\/li>\n<li>Find the x and y intercepts of a graphed equation<\/li>\n<li>Use the distance and midpoint formulas<\/li>\n<\/ul>\n<h3>Equations of Lines<\/h3>\n<ul>\n<li>Write equations of lines in slope-intercept, point-slope, and standard forms<\/li>\n<li>Identify the equations and graphs of horizontal and vertical lines<\/li>\n<li>Determine whether two lines are parallel, perpendicular, or neither<\/li>\n<li>Write equations of lines that are parallel or perpendicular to another line<\/li>\n<\/ul>\n<h3>Models and Applications of Linear Equations<\/h3>\n<ul>\n<li>Develop a problem solving method<\/li>\n<li>Write an equation to model an application<\/li>\n<li>Solve distance, rate and time problems<\/li>\n<li>Solve perimeter, area, and volume problems<\/li>\n<\/ul>\n<h2>Module 4: Equations and Inequalities<\/h2>\n<h3>Equation-Solving Techniques<\/h3>\n<ul>\n<li>Solve equations involving rational exponents.<\/li>\n<li>Solve equations using factoring.<\/li>\n<li>Solve radical equations.<\/li>\n<li>Solve absolute value equations<\/li>\n<\/ul>\n<h3>Models and Applications<\/h3>\n<ul>\n<li>Set up a linear equation to solve a real-world application.<\/li>\n<li>Use a formula to solve a real-world application.<\/li>\n<\/ul>\n<h3>Quadratic Equations<\/h3>\n<ul>\n<li>Solve quadratic equations by factoring.<\/li>\n<li>Solve quadratic equations by the square root property.<\/li>\n<li>Solve quadratic equations by completing the square.<\/li>\n<li>Solve quadratic equations by using the quadratic formula.<\/li>\n<\/ul>\n<h3>Linear Inequalities and Absolute Value Inequalities<\/h3>\n<ul>\n<li>Use interval notation.<\/li>\n<li>Use properties of inequalities.<\/li>\n<li>Solve inequalities in one variable algebraically.<\/li>\n<li>Solve absolute value inequalities<\/li>\n<\/ul>\n<h2>Module 5: Function Basics<\/h2>\n<h3>Characteristics of Functions and Their Graphs<\/h3>\n<ul>\n<li>Determine whether a relation represents a function.<\/li>\n<li>Find the value of a function.<\/li>\n<li>Determine whether a function is one-to-one.<\/li>\n<li>Use the vertical line test to identify functions.<\/li>\n<li>Graph the functions listed in the library of functions<\/li>\n<\/ul>\n<h3>Domain and Range of Functions<\/h3>\n<ul>\n<li>Find the domain of a function defined by an equation<\/li>\n<li>Write Domain and Range Using Standard Notations<\/li>\n<li>Find Domain and Range from a Graph<\/li>\n<li>Define Domain and Range of Toolkit Functions<\/li>\n<li>Graph Piecewise-Defined Functions<\/li>\n<\/ul>\n<h3>Rates of Change and Behavior of Graphs<\/h3>\n<ul>\n<li>Find the average rate of change of a function.<\/li>\n<li>Use a graph to determine where a function is increasing, decreasing, or constant.<\/li>\n<li>Use a graph to locate local maxima and local minima.<\/li>\n<li>Use a graph to locate the absolute maximum and absolute minimum.<\/li>\n<\/ul>\n<h2>Module 6:\u00a0Algebraic Operations on Functions<\/h2>\n<h3>Compositions of Functions<\/h3>\n<ul>\n<li>Combine functions using algebraic operations.<\/li>\n<li>Create a new function by composition of functions.<\/li>\n<li>Evaluate composite functions.<\/li>\n<li>Find the domain of a composite function.<\/li>\n<li>Decompose a composite function into its component functions.<\/li>\n<\/ul>\n<h3>Transformations of Functions<\/h3>\n<ul>\n<li>Graph functions using vertical and horizontal shifts.<\/li>\n<li>Graph functions using reflections about the [latex]x[\/latex] -axis and the [latex]y[\/latex] -axis.<\/li>\n<li>Determine whether a function is even, odd, or neither from its graph.<\/li>\n<li>Graph functions using compressions and stretches.<\/li>\n<li>Combine transformations.<\/li>\n<\/ul>\n<h3>Inverse Functions<\/h3>\n<ul>\n<li>Verify inverse functions.<\/li>\n<li>Determine the domain and range of an inverse function, and restrict the domain of a function to make it one-to-one.<\/li>\n<li>Find or evaluate the inverse of a function.<\/li>\n<li>Use the graph of a one-to-one function to graph its inverse function on the same axes.<\/li>\n<\/ul>\n<h2>Module 7: Linear and Absolute Value Functions<\/h2>\n<h3>Linear Functions<\/h3>\n<ul>\n<li>Represent a linear function with an equation, words, a table and a graph<\/li>\n<li>Determine whether a linear function is increasing, decreasing, or constant.<\/li>\n<li>Write and interpret a linear function.<\/li>\n<\/ul>\n<h3>Graphs of Linear Functions<\/h3>\n<ul>\n<li>Graph linear functions by plotting points, using the slope and y-intercept, and by using transformations<\/li>\n<li>Write the equation of a linear function given it&#8217;s graph, including vertical and horizontal lines, match linear equations with their graphs<\/li>\n<li>Find the equations of vertical and horizontal lines<\/li>\n<li>Graph an absolute value function, find it&#8217;s intercepts<\/li>\n<\/ul>\n<h3>Modeling With Linear Functions<\/h3>\n<ul>\n<li>Identify steps for modeling and solving.<\/li>\n<li>Build linear models from verbal descriptions.<\/li>\n<li>Draw and interpret scatter plots.<\/li>\n<li>Find the line of best fit using the Desmos calculator.<\/li>\n<li>Distinguish between linear and nonlinear relations.<\/li>\n<li>Use a linear model to make predictions.<\/li>\n<\/ul>\n<h2>Module 8:\u00a0Quadratic Functions<\/h2>\n<h3>Complex Numbers<\/h3>\n<ul>\n<li style=\"font-weight: 400;\">Express square roots of negative numbers as multiples of\u2009i<\/li>\n<li style=\"font-weight: 400;\">Plot complex numbers on the complex plane<\/li>\n<li style=\"font-weight: 400;\">Add and subtract complex numbers<\/li>\n<li style=\"font-weight: 400;\">Multiply and divide complex numbers<\/li>\n<\/ul>\n<h3>Graphs of Quadratic Functions<\/h3>\n<ul>\n<li style=\"font-weight: 400;\">Recognize characteristics of parabolas<\/li>\n<li style=\"font-weight: 400;\">Understand how the graph of a parabola is related to its quadratic function<\/li>\n<\/ul>\n<h3>Analysis of Quadratic Functions<\/h3>\n<ul>\n<li style=\"font-weight: 400;\">Use the quadratic formula and factoring to find both real and complex roots (x-intercepts) of quadratic functions<\/li>\n<li style=\"font-weight: 400;\">Use algebra to find the y-intercepts of a quadratic function<\/li>\n<li style=\"font-weight: 400;\">Solve problems involving the roots and intercepts of a quadratic function<\/li>\n<li style=\"font-weight: 400;\">Use the discriminant to determine the nature (real or complex) and quantity of solutions to quadratic equations<\/li>\n<li style=\"font-weight: 400;\">Determine a quadratic function\u2019s minimum or maximum value<\/li>\n<li style=\"font-weight: 400;\">Solve problems involving a quadratic function\u2019s minimum or maximum value<\/li>\n<\/ul>\n<h2>Module 9: Power and Polynomial Functions<\/h2>\n<h3>Characteristics of Power and Polynomial Functions<\/h3>\n<ul>\n<li>Identify power functions.<\/li>\n<li>Identify end behavior of power functions.<\/li>\n<li>Identify polynomial functions.<\/li>\n<li>Identify the degree and leading coefficient of polynomial functions.<\/li>\n<li>Identify local behavior of polynomial functions.<\/li>\n<\/ul>\n<h3>Graphs of Polynomial Functions<\/h3>\n<ul>\n<li>Identify zeros of polynomial functions with even and odd multiplicity<\/li>\n<li>Use the degree of a polynomial\u00a0to determine the number of turning points of its graph<\/li>\n<li>Draw the graph of a polynomial function using end behavior, turning points, intercepts, and the intermediate value theorem<\/li>\n<li>Write the equation of a polynomial function given it&#8217;s graph<\/li>\n<\/ul>\n<h3>Divide Polynomials<\/h3>\n<ul>\n<li>Use long division to divide polynomials.<\/li>\n<li>Use synthetic division to divide polynomials.<\/li>\n<\/ul>\n<h3>Methods for Finding Zeros of Polynomials<\/h3>\n<ul>\n<li>Evaluate a polynomial using the Remainder Theorem.<\/li>\n<li>Use the Factor Theorem to solve a polynomial equation.<\/li>\n<li>Use the Rational Zero Theorem to find rational zeros.<\/li>\n<li>Find zeros of a polynomial function.<\/li>\n<li>Use the Linear Factorization Theorem to find polynomials with given zeros.<\/li>\n<li>Use Descartes\u2019 Rule of Signs.<\/li>\n<li>Solve real-world applications of polynomial equations<\/li>\n<\/ul>\n<h2>Module 10: Rational and Radical Functions<\/h2>\n<h3>Rational Functions<\/h3>\n<ul>\n<li>Use arrow notation to describe end behavior of rational functions<\/li>\n<li>Solve applied problems involving rational functions.<\/li>\n<li>Find the domains of rational functions.<\/li>\n<li>Identify vertical and horizontal asymptotes of graphs of rational functions<\/li>\n<li>Graph rational functions.<\/li>\n<\/ul>\n<h3>Radical Functions<\/h3>\n<ul>\n<li>Find the inverse of a polynomial function.<\/li>\n<li>Restrict the domain to find the inverse of a polynomial function.<\/li>\n<\/ul>\n<h3>Variation<\/h3>\n<ul>\n<li>Solve direct variation problems.<\/li>\n<li>Solve inverse variation problems.<\/li>\n<li>Solve problems involving joint variation.<\/li>\n<\/ul>\n<h2>Module 11:\u00a0Exponential and Logarithmic Functions<\/h2>\n<h3>Exponential Functions<\/h3>\n<ul>\n<li>Evaluate an exponential growth function with different bases<\/li>\n<li>Use a compound interest Formula<\/li>\n<li>Write an exponential function<\/li>\n<li>Find an exponential function given a graph<\/li>\n<li>Use a graphing calculator to find an exponential function<\/li>\n<li>Find an exponential function that models continuous growth or decay<\/li>\n<\/ul>\n<h3>Graphs of Exponential Functions<\/h3>\n<ul>\n<li>Graph exponential functions, determine whether a graph represents exponential growth or decay<\/li>\n<li>Graph exponential functions using transformations.<\/li>\n<\/ul>\n<h3>Logarithmic Functions<\/h3>\n<ul>\n<li>Convert from logarithmic to exponential form.<\/li>\n<li>Convert from exponential to logarithmic form.<\/li>\n<li>Evaluate common and natural logarithms.<\/li>\n<\/ul>\n<h3>Graphs of Logarithmic Functions<\/h3>\n<ul>\n<li>Identify the domain of a logarithmic function.<\/li>\n<li>Graph logarithmic functions using transformations, and identify intercepts and the vertical asymptote<\/li>\n<li>Identify why and how a logarithmic function is an inverse of an exponential function<\/li>\n<\/ul>\n<h2>Module 12:\u00a0Exponential and Logarithmic Equations and Models<\/h2>\n<h3>Logarithmic Properties<\/h3>\n<ul>\n<li>Use power, product, and quotient rules to expand and condense logarithms<\/li>\n<li>Use the change-of-base formula for logarithms.<\/li>\n<\/ul>\n<h3>Exponential and Logarithmic Equations<\/h3>\n<ul>\n<li>Use like bases to solve exponential equations.<\/li>\n<li>Use logarithms to solve exponential equations.<\/li>\n<li>Use the definition of a logarithm to solve logarithmic equations.<\/li>\n<li>Use the one-to-one property of logarithms to solve logarithmic equations.<\/li>\n<li>Solve applied problems involving exponential and logarithmic equations.<\/li>\n<\/ul>\n<h3>Exponential and Logarithmic Models<\/h3>\n<ul>\n<li>Model exponential growth and decay.<\/li>\n<li>Use Newton\u2019s Law of Cooling.<\/li>\n<li>Use logistic-growth models.<\/li>\n<li>Choose an appropriate model for data.<\/li>\n<li>Express an exponential model in base <em>e<\/em>.<\/li>\n<\/ul>\n<h3>Fitting Exponential Models to Data<\/h3>\n<ul>\n<li>Build an exponential model from data.<\/li>\n<li>Build a logarithmic model from data.<\/li>\n<li>Build a logistic model from data.<\/li>\n<\/ul>\n<h2>Module 13:\u00a0Systems of Equations and Inequalities<\/h2>\n<h3>Systems of Linear Equations: Two Variables<\/h3>\n<ul>\n<li>Solve systems of equations by graphing,\u00a0substitution, and\u00a0addition.<\/li>\n<li>Identify inconsistent systems of equations containing two variables.<\/li>\n<li>Express the solution of a system of dependent equations containing two variables using standard notations.<\/li>\n<\/ul>\n<h3>Systems of Nonlinear Equations and Inequalities<\/h3>\n<ul>\n<li>Solve a system of nonlinear equations using substitution or elimination.<\/li>\n<li>Graph a nonlinear inequality.<\/li>\n<li>Graph a system of nonlinear inequalities.<\/li>\n<\/ul>\n<h3>Systems of Linear Equations: Three Variables<\/h3>\n<ul>\n<li>Solve systems of three equations in three variables.<\/li>\n<li>Identify inconsistent systems of equations containing three variables.<\/li>\n<li>Express the solution of a system of dependent equations containing three variables using standard notations.<\/li>\n<\/ul>\n<h3>Partial Fractions: an Application of Systems<\/h3>\n<ul>\n<li>Decompose \u2009 [latex]\\frac{{P( x )}}{{ Q( x )}}[\/latex] ,\u2009 where \u2009Q( x )\u2009 has only nonrepeated linear factors.<\/li>\n<li>Decompose \u2009[latex]\\frac{{P( x )}}{{ Q( x )}}[\/latex] ,\u2009 where \u2009Q( x )\u2009 has repeated linear factors.<\/li>\n<li>Decompose \u2009[latex]\\frac{{P( x )}}{{ Q( x )}}[\/latex] ,\u2009 where \u2009Q( x )\u2009 has a nonrepeated irreducible quadratic factor.<\/li>\n<li>Decompose \u2009[latex]\\frac{{P( x )}}{{ Q( x )}}[\/latex] ,\u2009 where \u2009Q( x )\u2009 has a repeated irreducible quadratic factor.<\/li>\n<\/ul>\n<h2>Module 14: Solve Systems With Matrices<\/h2>\n<h3>Matrices and Matrix Operations<\/h3>\n<ul>\n<li>Find the sum and difference of two matrices.<\/li>\n<li>Find scalar multiples of a matrix.<\/li>\n<li>Find the product of two matrices.<\/li>\n<\/ul>\n<h3>Gaussian Elimination<\/h3>\n<ul>\n<li>Write the augmented matrix of a system of equations.<\/li>\n<li>Write the system of equations from an augmented matrix.<\/li>\n<li>Perform row operations on a matrix.<\/li>\n<li>Solve a system of linear equations using matrices.<\/li>\n<\/ul>\n<h3>Solve Systems with Inverses<\/h3>\n<ul>\n<li>Find the inverse of a matrix.<\/li>\n<li>Solve a system of linear equations using an inverse matrix.<\/li>\n<\/ul>\n<h2>Module 15: Conic Sections<\/h2>\n<h3>The Ellipse<\/h3>\n<ul>\n<li>Write equations of ellipses in standard form.<\/li>\n<li>Graph ellipses centered at the origin.<\/li>\n<li>Graph ellipses not centered at the origin.<\/li>\n<li>Solve applied problems involving ellipses.<\/li>\n<\/ul>\n<h3>The Hyperbola<\/h3>\n<ul>\n<li>Locate a hyperbola\u2019s vertices and foci.<\/li>\n<li>Write equations of hyperbolas in standard form.<\/li>\n<li>Graph hyperbolas centered at the origin.<\/li>\n<li>Graph hyperbolas not centered at the origin.<\/li>\n<li>Solve applied problems involving hyperbolas.<\/li>\n<\/ul>\n<h3>The Parabola<\/h3>\n<ul>\n<li>Graph parabolas with vertices at the origin.<\/li>\n<li>Write equations of parabolas in standard form.<\/li>\n<li>Graph parabolas with vertices not at the origin.<\/li>\n<li>Solve applied problems involving parabolas.<\/li>\n<\/ul>\n<h2>Module 16:\u00a0Sequences and Series<\/h2>\n<h3>Sequences and Their Notations<\/h3>\n<ul>\n<li>Write the terms of a sequence defined by an explicit formula.<\/li>\n<li>Write the terms of a sequence defined by a recursive formula.<\/li>\n<li>Use factorial notation.<\/li>\n<\/ul>\n<h3>\u00a0Arithmetic Sequences<\/h3>\n<ul>\n<li>Find the common difference for an arithmetic sequence.<\/li>\n<li>Write terms of an arithmetic sequence.<\/li>\n<li>Use a recursive formula for an arithmetic sequence.<\/li>\n<li>Use an explicit formula for an arithmetic sequence.<\/li>\n<\/ul>\n<h3>Geometric Sequences<\/h3>\n<ul>\n<li>Find the common ratio for a geometric sequence.<\/li>\n<li>List the terms of a geometric sequence.<\/li>\n<li>Use a recursive formula for a geometric sequence.<\/li>\n<li>Use an explicit formula for a geometric sequence.<\/li>\n<\/ul>\n<h3>Series and Their Notations<\/h3>\n<ul>\n<li>Use summation notation.<\/li>\n<li>Use the formula for the sum of the \ufb01rst [latex]n[\/latex] terms of an arithmetic series.<\/li>\n<li>Use the formula for the sum of the \ufb01rst [latex]n[\/latex] terms of a geometric series.<\/li>\n<li>Use the formula for the sum of an in\ufb01nite geometric series.<\/li>\n<li>Solve annuity problems.<\/li>\n<\/ul>\n<h2>Module 17: Counting Principles<\/h2>\n<h3>Counting Principles<\/h3>\n<ul>\n<li>Solve counting problems using the Addition Principle and the\u00a0Multiplication Principle.<\/li>\n<li>Solve counting problems using permutations and combinations \u00a0involving n distinct objects.<\/li>\n<li>Find the number of subsets of a given set.<\/li>\n<li>Solve counting problems using permutations involving n non-distinct objects.<\/li>\n<li>Apply the Binomial Theorem<\/li>\n<\/ul>\n<h3>Probability<\/h3>\n<ul>\n<li>Construct probability models.<\/li>\n<li>Compute probabilities of equally likely outcomes.<\/li>\n<li>Compute probabilities of the union of two events.<\/li>\n<li>Use the complement rule to find probabilities.<\/li>\n<li>Compute probability using counting theory.<\/li>\n<\/ul>\n","protected":false},"author":31,"menu_order":1,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"front-matter-type":[],"contributor":[],"license":[],"class_list":["post-4340","front-matter","type-front-matter","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/front-matter\/4340","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/front-matter"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/wp\/v2\/types\/front-matter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/wp\/v2\/users\/31"}],"version-history":[{"count":1,"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/front-matter\/4340\/revisions"}],"predecessor-version":[{"id":4341,"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/front-matter\/4340\/revisions\/4341"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/front-matter\/4340\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/wp\/v2\/media?parent=4340"}],"wp:term":[{"taxonomy":"front-matter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/front-matter-type?post=4340"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/wp\/v2\/contributor?post=4340"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/wp\/v2\/license?post=4340"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}