Module 1: Algebra Essentials<\/h2>\r\nEvaluate and simplify expressions that contain both real numbers and variables<\/h3>\r\n\r\n \t- Classify a real number<\/li>\r\n \t
- Perform calculations using order of operations.<\/li>\r\n \t
- Use the properties of real numbers<\/li>\r\n \t
- Evaluate and simplify algebraic expressions.<\/li>\r\n \t
- Use the rules of exponents to simplify exponential expressions<\/li>\r\n \t
- Use scientific notation<\/li>\r\n \t
- Evaluate and simplify square roots<\/li>\r\n \t
- Rationalize a denominator that contains a square root<\/li>\r\n \t
- Rewrite a radical expression using rational exponents<\/li>\r\n<\/ul>\r\n
Module 2: Polynomial and Rational Expressions<\/h2>\r\n\r\n \t- Identify the degree, leading coefficient, and leading term of a polynomial expression<\/li>\r\n \t
- Perform algebraic operations on polynomial expressions<\/li>\r\n \t
- Identify the greatest common factor of a polynomial expression<\/li>\r\n \t
- Factor a wide variety of polynomials including those with fractional or negative exponents<\/li>\r\n \t
- Simplify and perform algebraic operations on rational expressions<\/li>\r\n<\/ul>\r\n
Module 3: The Rectangular Coordinate System and Equations of Lines<\/h2>\r\n\r\n \t- Plot ordered pairs, and graph equations by plotting points<\/li>\r\n \t
- Use a graphing utility to graph equations<\/li>\r\n \t
- Find the x and y intercepts of a graphed equation<\/li>\r\n \t
- Use the distance and midpoint formulas<\/li>\r\n \t
- Write equations of lines in slope-intercept, point-slope, and standard forms<\/li>\r\n \t
- Identify the equations and graphs of horizontal and vertical lines<\/li>\r\n \t
- Determine whether two lines are parallel, perpendicular, or neither<\/li>\r\n \t
- Write equations of lines that are parallel or perpendicular to another line<\/li>\r\n \t
- Develop a problem solving method<\/li>\r\n \t
- Write an equation to model an application<\/li>\r\n \t
- Solve distance, rate and time problems<\/li>\r\n \t
- Solve perimeter, area, and volume problems<\/li>\r\n<\/ul>\r\n
Module 4: Equations and Inequalities<\/h2>\r\n\r\n \t- Solve equations involving rational exponents<\/li>\r\n \t
- Solve equations using factoring<\/li>\r\n \t
- Solve radical equations<\/li>\r\n \t
- Solve absolute value equations<\/li>\r\n \t
- Set up a linear equation to solve a real-world application<\/li>\r\n \t
- Use a formula to solve a real-world application<\/li>\r\n \t
- Solve quadratic equations by factoring<\/li>\r\n \t
- Solve quadratic equations by the square root property<\/li>\r\n \t
- Solve quadratic equations by completing the square<\/li>\r\n \t
- Solve quadratic equations by using the quadratic formula<\/li>\r\n \t
- Use interval notation<\/li>\r\n \t
- Use properties of inequalities<\/li>\r\n \t
- Solve inequalities in one variable algebraically<\/li>\r\n \t
- Solve absolute value inequalities<\/li>\r\n<\/ul>\r\n
Module 5: Function Basics<\/h2>\r\n\r\n \t- Determine whether a relation represents a function<\/li>\r\n \t
- Find the value of a function<\/li>\r\n \t
- Determine whether a function is one-to-one<\/li>\r\n \t
- Use the vertical line test to identify functions<\/li>\r\n \t
- Graph the functions listed in the library of functions<\/li>\r\n \t
- Find the domain of a function defined by an equation<\/li>\r\n \t
- Write Domain and Range Using Standard Notations<\/li>\r\n \t
- Find Domain and Range from a Graph<\/li>\r\n \t
- Define Domain and Range of Toolkit Functions<\/li>\r\n \t
- Graph Piecewise-Defined Functions<\/li>\r\n \t
- Find the average rate of change of a function<\/li>\r\n \t
- Use a graph to determine where a function is increasing, decreasing, or constant<\/li>\r\n \t
- Use a graph to locate local maxima and local minima<\/li>\r\n \t
- Use a graph to locate the absolute maximum and absolute minimum<\/li>\r\n<\/ul>\r\n
Module 6:\u00a0Algebraic Operations on Functions<\/h2>\r\n\r\n \t- Combine functions using algebraic operations<\/li>\r\n \t
- Create a new function by composition of functions<\/li>\r\n \t
- Evaluate composite functions<\/li>\r\n \t
- Find the domain of a composite function<\/li>\r\n \t
- Decompose a composite function into its component functions<\/li>\r\n \t
- Graph functions using vertical and horizontal shifts<\/li>\r\n \t
- Graph functions using reflections about the [latex]x[\/latex] -axis and the [latex]y[\/latex] -axis<\/li>\r\n \t
- Determine whether a function is even, odd, or neither from its graph<\/li>\r\n \t
- Graph functions using compressions and stretches<\/li>\r\n \t
- Combine transformations<\/li>\r\n \t
- Verify inverse functions<\/li>\r\n \t
- 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
- Find or evaluate the inverse of a function<\/li>\r\n \t
- Use the graph of a one-to-one function to graph its inverse function on the same axes<\/li>\r\n<\/ul>\r\n
Module 7: Linear and Absolute Value Functions<\/h2>\r\n\r\n \t- Represent a linear function with an equation, words, a table and a graph<\/li>\r\n \t
- Determine whether a linear function is increasing, decreasing, or constant.<\/li>\r\n \t
- Write and interpret a linear function.<\/li>\r\n<\/ul>\r\n
\r\n \t- Graph linear functions by plotting points, using the slope and y-intercept, and by using transformations<\/li>\r\n \t
- 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
- Find the equations of vertical and horizontal lines<\/li>\r\n \t
- Graph an absolute value function, find it's intercepts<\/li>\r\n<\/ul>\r\n
\r\n \t- Identify steps for modeling and solving.<\/li>\r\n \t
- Build linear models from verbal descriptions.<\/li>\r\n \t
- Draw and interpret scatter plots.<\/li>\r\n \t
- Find the line of best fit using an online graphing tool.<\/li>\r\n \t
- Distinguish between linear and nonlinear relations.<\/li>\r\n \t
- Use a linear model to make predictions.<\/li>\r\n<\/ul>\r\n
Module 8:\u00a0Quadratic Functions<\/h2>\r\n\r\n \t- Express square roots of negative numbers as multiples of\u2009i<\/li>\r\n \t
- Plot complex numbers on the complex plane<\/li>\r\n \t
- Add and subtract complex numbers<\/li>\r\n \t
- Multiply and divide complex numbers<\/li>\r\n<\/ul>\r\n
\r\n \t- Recognize characteristics of parabolas<\/li>\r\n \t
- Understand how the graph of a parabola is related to its quadratic function<\/li>\r\n<\/ul>\r\n
\r\n \t- Use the quadratic formula and factoring to find both real and complex roots (x-intercepts) of quadratic functions<\/li>\r\n \t
- Use algebra to find the y-intercepts of a quadratic function<\/li>\r\n \t
- Solve problems involving the roots and intercepts of a quadratic function<\/li>\r\n \t
- Use the discriminant to determine the nature (real or complex) and quantity of solutions to quadratic equations<\/li>\r\n \t
- Determine a quadratic function\u2019s minimum or maximum value<\/li>\r\n \t
- Solve problems involving a quadratic function\u2019s minimum or maximum value<\/li>\r\n<\/ul>\r\n
Module 9: Power and Polynomial Functions<\/h2>\r\n\r\n \t- Identify power functions.<\/li>\r\n \t
- Identify end behavior of power functions.<\/li>\r\n \t
- Identify polynomial functions.<\/li>\r\n \t
- Identify the degree and leading coefficient of polynomial functions.<\/li>\r\n \t
- Identify local behavior of polynomial functions.<\/li>\r\n<\/ul>\r\n
\r\n \t- Identify zeros of polynomial functions with even and odd multiplicity<\/li>\r\n \t
- Use the degree of a polynomial\u00a0to determine the number of turning points of its graph<\/li>\r\n \t
- Draw the graph of a polynomial function using end behavior, turning points, intercepts, and the intermediate value theorem<\/li>\r\n \t
- Write the equation of a polynomial function given it's graph<\/li>\r\n<\/ul>\r\n
\r\n \t- Use long division to divide polynomials.<\/li>\r\n \t
- Use synthetic division to divide polynomials.<\/li>\r\n<\/ul>\r\n
\r\n \t- Evaluate a polynomial using the Remainder Theorem.<\/li>\r\n \t
- Use the Factor Theorem to solve a polynomial equation.<\/li>\r\n \t
- Use the Rational Zero Theorem to find rational zeros.<\/li>\r\n \t
- Find zeros of a polynomial function.<\/li>\r\n \t
- Use the Linear Factorization Theorem to find polynomials with given zeros.<\/li>\r\n \t
- Use Descartes\u2019 Rule of Signs.<\/li>\r\n \t
- Solve real-world applications of polynomial equations<\/li>\r\n<\/ul>\r\n
Module 10: Rational and Radical Functions<\/h2>\r\n\r\n \t- Use arrow notation to describe end behavior of rational functions<\/li>\r\n \t
- Solve applied problems involving rational functions.<\/li>\r\n \t
- Find the domains of rational functions.<\/li>\r\n \t
- Identify vertical and horizontal asymptotes of graphs of rational functions<\/li>\r\n \t
- Graph rational functions.<\/li>\r\n \t
- Find the inverse of a polynomial function.<\/li>\r\n \t
- Restrict the domain to find the inverse of a polynomial function.<\/li>\r\n \t
- Solve direct variation problems.<\/li>\r\n \t
- Solve inverse variation problems.<\/li>\r\n \t
- Solve problems involving joint variation.<\/li>\r\n<\/ul>\r\n
Module 11:\u00a0Exponential and Logarithmic Functions<\/h2>\r\n\r\n \t- Evaluate an exponential growth function with different bases<\/li>\r\n \t
- Use a compound interest Formula<\/li>\r\n \t
- Write an exponential function<\/li>\r\n \t
- Find an exponential function given a graph<\/li>\r\n \t
- Use a graphing calculator to find an exponential function<\/li>\r\n \t
- Find an exponential function that models continuous growth or decay<\/li>\r\n \t
- Graph exponential functions, determine whether a graph represents exponential growth or decay<\/li>\r\n \t
- Graph exponential functions using transformations.<\/li>\r\n \t
- Convert from logarithmic to exponential form.<\/li>\r\n \t
- Convert from exponential to logarithmic form.<\/li>\r\n \t
- Evaluate common and natural logarithms.<\/li>\r\n \t
- Identify the domain of a logarithmic function.<\/li>\r\n \t
- Graph logarithmic functions using transformations, and identify intercepts and the vertical asymptote<\/li>\r\n \t
- Identify why and how a logarithmic function is an inverse of an exponential function<\/li>\r\n<\/ul>\r\n
Module 12:\u00a0Exponential and Logarithmic Equations and Models<\/h2>\r\n\r\n \t- Use power, product, and quotient rules to expand and condense logarithms<\/li>\r\n \t
- Use the change-of-base formula for logarithms.<\/li>\r\n \t
- Use like bases to solve exponential equations.<\/li>\r\n \t
- Use logarithms to solve exponential equations.<\/li>\r\n \t
- Use the definition of a logarithm to solve logarithmic equations.<\/li>\r\n \t
- Use the one-to-one property of logarithms to solve logarithmic equations.<\/li>\r\n \t
- Solve applied problems involving exponential and logarithmic equations.<\/li>\r\n \t
- Model exponential growth and decay.<\/li>\r\n \t
- Use Newton\u2019s Law of Cooling.<\/li>\r\n \t
- Use logistic-growth models.<\/li>\r\n \t
- Choose an appropriate model for data.<\/li>\r\n \t
- Express an exponential model in base e<\/em>.<\/li>\r\n \t
- Build an exponential model from data.<\/li>\r\n<\/ul>\r\n
Module 13:\u00a0Systems of Equations and Inequalities<\/h2>\r\n\r\n \t- Solve systems of equations by graphing,\u00a0substitution, and\u00a0addition.<\/li>\r\n \t
- Identify inconsistent systems of equations containing two variables.<\/li>\r\n \t
- Express the solution of a system of dependent equations containing two variables using standard notations.<\/li>\r\n<\/ul>\r\n
\r\n \t- Solve a system of nonlinear equations using substitution or elimination.<\/li>\r\n \t
- Graph a nonlinear inequality.<\/li>\r\n \t
- Graph a system of nonlinear inequalities.<\/li>\r\n<\/ul>\r\n
\r\n \t- Solve systems of three equations in three variables.<\/li>\r\n \t
- Identify inconsistent systems of equations containing three variables.<\/li>\r\n \t
- Express the solution of a system of dependent equations containing three variables using standard notations.<\/li>\r\n<\/ul>\r\n
\r\n \t- Decompose \u2009 [latex]\\frac{{P( x )}}{{ Q( x )}}[\/latex] ,\u2009 where \u2009Q( x )\u2009 has only nonrepeated linear factors.<\/li>\r\n \t
- Decompose \u2009[latex]\\frac{{P( x )}}{{ Q( x )}}[\/latex] ,\u2009 where \u2009Q( x )\u2009 has repeated linear factors.<\/li>\r\n \t
- Decompose \u2009[latex]\\frac{{P( x )}}{{ Q( x )}}[\/latex] ,\u2009 where \u2009Q( x )\u2009 has a nonrepeated irreducible quadratic factor.<\/li>\r\n \t
- 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
Module 14: Solve Systems With Matrices<\/h2>\r\n\r\n \t- Find the sum and difference of two matrices.<\/li>\r\n \t
- Find scalar multiples of a matrix.<\/li>\r\n \t
- Find the product of two matrices.<\/li>\r\n \t
- Write the augmented matrix of a system of equations.<\/li>\r\n \t
- Write the system of equations from an augmented matrix.<\/li>\r\n \t
- Perform row operations on a matrix.<\/li>\r\n \t
- Solve a system of linear equations using matrices.<\/li>\r\n \t
- Find the inverse of a matrix.<\/li>\r\n \t
- Solve a system of linear equations using an inverse matrix.<\/li>\r\n<\/ul>\r\n
Module 15: Conic Sections<\/h2>\r\n\r\n \t- Write equations of ellipses in standard form<\/li>\r\n \t
- Graph ellipses centered at the origin<\/li>\r\n \t
- Graph ellipses not centered at the origin<\/li>\r\n \t
- Solve applied problems involving ellipses<\/li>\r\n \t
- Locate a hyperbola\u2019s vertices and foci<\/li>\r\n \t
- Write equations of hyperbolas in standard form<\/li>\r\n \t
- Graph hyperbolas centered at the origin<\/li>\r\n \t
- Graph hyperbolas not centered at the origin<\/li>\r\n \t
- Solve applied problems involving hyperbolas<\/li>\r\n \t
- Graph parabolas with vertices at the origin<\/li>\r\n \t
- Write equations of parabolas in standard form<\/li>\r\n \t
- Graph parabolas with vertices not at the origin<\/li>\r\n \t
- Solve applied problems involving parabolas<\/li>\r\n<\/ul>\r\n
Module 16:\u00a0Sequences and Series<\/h2>\r\n\r\n \t- Write the terms of a sequence defined by an explicit formula<\/li>\r\n \t
- Write the terms of a sequence defined by a recursive formula<\/li>\r\n \t
- Use factorial notation<\/li>\r\n \t
- Find the common difference for an arithmetic sequence<\/li>\r\n \t
- Write terms of an arithmetic sequence<\/li>\r\n \t
- Use a recursive formula for an arithmetic sequence<\/li>\r\n \t
- Use an explicit formula for an arithmetic sequence<\/li>\r\n \t
- Find the common ratio for a geometric sequence<\/li>\r\n \t
- List the terms of a geometric sequence<\/li>\r\n \t
- Use a recursive formula for a geometric sequence<\/li>\r\n \t
- Use an explicit formula for a geometric sequence<\/li>\r\n \t
- Use summation notation<\/li>\r\n \t
- Use the formula for the sum of the \ufb01rst [latex]n[\/latex] terms of an arithmetic series<\/li>\r\n \t
- Use the formula for the sum of the \ufb01rst [latex]n[\/latex] terms of a geometric series<\/li>\r\n \t
- Use the formula for the sum of an in\ufb01nite geometric series<\/li>\r\n \t
- Solve annuity problems<\/li>\r\n<\/ul>\r\n
Module 17: Probability and Counting Principles<\/h2>\r\n\r\n \t- Solve counting problems using the Addition Principle and the\u00a0Multiplication Principle<\/li>\r\n \t
- Solve counting problems using permutations and combinations \u00a0involving n distinct objects<\/li>\r\n \t
- Find the number of subsets of a given set<\/li>\r\n \t
- Solve counting problems using permutations involving n non-distinct objects<\/li>\r\n \t
- Apply the Binomial Theorem<\/li>\r\n \t
- Construct probability models<\/li>\r\n \t
- Compute probabilities of equally likely outcomes<\/li>\r\n \t
- Compute probabilities of the union of two events<\/li>\r\n \t
- Use the complement rule to find probabilities<\/li>\r\n \t
- Compute probability using counting theory<\/li>\r\n<\/ul>","rendered":"
![\"icon](\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1916\/2017\/12\/22205107\/outcomes.jpg\")
<\/p>\n
The content, assignments, and assessments for College Algebra are aligned to the following learning outcomes. A full list of course learning outcomes can be viewed here: College Algebra Learning Outcomes.<\/a><\/p>\nModule 1: Algebra Essentials<\/h2>\nEvaluate and simplify expressions that contain both real numbers and variables<\/h3>\n\n- Classify a real number<\/li>\n
- Perform calculations using order of operations.<\/li>\n
- Use the properties of real numbers<\/li>\n
- Evaluate and simplify algebraic expressions.<\/li>\n
- Use the rules of exponents to simplify exponential expressions<\/li>\n
- Use scientific notation<\/li>\n
- Evaluate and simplify square roots<\/li>\n
- Rationalize a denominator that contains a square root<\/li>\n
- Rewrite a radical expression using rational exponents<\/li>\n<\/ul>\n
Module 2: Polynomial and Rational Expressions<\/h2>\n\n- Identify the degree, leading coefficient, and leading term of a polynomial expression<\/li>\n
- Perform algebraic operations on polynomial expressions<\/li>\n
- Identify the greatest common factor of a polynomial expression<\/li>\n
- Factor a wide variety of polynomials including those with fractional or negative exponents<\/li>\n
- Simplify and perform algebraic operations on rational expressions<\/li>\n<\/ul>\n
Module 3: The Rectangular Coordinate System and Equations of Lines<\/h2>\n\n- Plot ordered pairs, and graph equations by plotting points<\/li>\n
- Use a graphing utility to graph equations<\/li>\n
- Find the x and y intercepts of a graphed equation<\/li>\n
- Use the distance and midpoint formulas<\/li>\n
- Write equations of lines in slope-intercept, point-slope, and standard forms<\/li>\n
- Identify the equations and graphs of horizontal and vertical lines<\/li>\n
- Determine whether two lines are parallel, perpendicular, or neither<\/li>\n
- Write equations of lines that are parallel or perpendicular to another line<\/li>\n
- Develop a problem solving method<\/li>\n
- Write an equation to model an application<\/li>\n
- Solve distance, rate and time problems<\/li>\n
- Solve perimeter, area, and volume problems<\/li>\n<\/ul>\n
Module 4: Equations and Inequalities<\/h2>\n\n- Solve equations involving rational exponents<\/li>\n
- Solve equations using factoring<\/li>\n
- Solve radical equations<\/li>\n
- Solve absolute value equations<\/li>\n
- Set up a linear equation to solve a real-world application<\/li>\n
- Use a formula to solve a real-world application<\/li>\n
- Solve quadratic equations by factoring<\/li>\n
- Solve quadratic equations by the square root property<\/li>\n
- Solve quadratic equations by completing the square<\/li>\n
- Solve quadratic equations by using the quadratic formula<\/li>\n
- Use interval notation<\/li>\n
- Use properties of inequalities<\/li>\n
- Solve inequalities in one variable algebraically<\/li>\n
- Solve absolute value inequalities<\/li>\n<\/ul>\n
Module 5: Function Basics<\/h2>\n\n- Determine whether a relation represents a function<\/li>\n
- Find the value of a function<\/li>\n
- Determine whether a function is one-to-one<\/li>\n
- Use the vertical line test to identify functions<\/li>\n
- Graph the functions listed in the library of functions<\/li>\n
- Find the domain of a function defined by an equation<\/li>\n
- Write Domain and Range Using Standard Notations<\/li>\n
- Find Domain and Range from a Graph<\/li>\n
- Define Domain and Range of Toolkit Functions<\/li>\n
- Graph Piecewise-Defined Functions<\/li>\n
- Find the average rate of change of a function<\/li>\n
- Use a graph to determine where a function is increasing, decreasing, or constant<\/li>\n
- Use a graph to locate local maxima and local minima<\/li>\n
- Use a graph to locate the absolute maximum and absolute minimum<\/li>\n<\/ul>\n
Module 6:\u00a0Algebraic Operations on Functions<\/h2>\n\n- Combine functions using algebraic operations<\/li>\n
- Create a new function by composition of functions<\/li>\n
- Evaluate composite functions<\/li>\n
- Find the domain of a composite function<\/li>\n
- Decompose a composite function into its component functions<\/li>\n
- Graph functions using vertical and horizontal shifts<\/li>\n
- Graph functions using reflections about the [latex]x[\/latex] -axis and the [latex]y[\/latex] -axis<\/li>\n
- Determine whether a function is even, odd, or neither from its graph<\/li>\n
- Graph functions using compressions and stretches<\/li>\n
- Combine transformations<\/li>\n
- Verify inverse functions<\/li>\n
- Determine the domain and range of an inverse function, and restrict the domain of a function to make it one-to-one<\/li>\n
- Find or evaluate the inverse of a function<\/li>\n
- Use the graph of a one-to-one function to graph its inverse function on the same axes<\/li>\n<\/ul>\n
Module 7: Linear and Absolute Value Functions<\/h2>\n\n- Represent a linear function with an equation, words, a table and a graph<\/li>\n
- Determine whether a linear function is increasing, decreasing, or constant.<\/li>\n
- Write and interpret a linear function.<\/li>\n<\/ul>\n
\n- Graph linear functions by plotting points, using the slope and y-intercept, and by using transformations<\/li>\n
- Write the equation of a linear function given it’s graph, including vertical and horizontal lines, match linear equations with their graphs<\/li>\n
- Find the equations of vertical and horizontal lines<\/li>\n
- Graph an absolute value function, find it’s intercepts<\/li>\n<\/ul>\n
\n- Identify steps for modeling and solving.<\/li>\n
- Build linear models from verbal descriptions.<\/li>\n
- Draw and interpret scatter plots.<\/li>\n
- Find the line of best fit using an online graphing tool.<\/li>\n
- Distinguish between linear and nonlinear relations.<\/li>\n
- Use a linear model to make predictions.<\/li>\n<\/ul>\n
Module 8:\u00a0Quadratic Functions<\/h2>\n\n- Express square roots of negative numbers as multiples of\u2009i<\/li>\n
- Plot complex numbers on the complex plane<\/li>\n
- Add and subtract complex numbers<\/li>\n
- Multiply and divide complex numbers<\/li>\n<\/ul>\n
\n- Recognize characteristics of parabolas<\/li>\n
- Understand how the graph of a parabola is related to its quadratic function<\/li>\n<\/ul>\n
\n- Use the quadratic formula and factoring to find both real and complex roots (x-intercepts) of quadratic functions<\/li>\n
- Use algebra to find the y-intercepts of a quadratic function<\/li>\n
- Solve problems involving the roots and intercepts of a quadratic function<\/li>\n
- Use the discriminant to determine the nature (real or complex) and quantity of solutions to quadratic equations<\/li>\n
- Determine a quadratic function\u2019s minimum or maximum value<\/li>\n
- Solve problems involving a quadratic function\u2019s minimum or maximum value<\/li>\n<\/ul>\n
Module 9: Power and Polynomial Functions<\/h2>\n\n- Identify power functions.<\/li>\n
- Identify end behavior of power functions.<\/li>\n
- Identify polynomial functions.<\/li>\n
- Identify the degree and leading coefficient of polynomial functions.<\/li>\n
- Identify local behavior of polynomial functions.<\/li>\n<\/ul>\n
\n- Identify zeros of polynomial functions with even and odd multiplicity<\/li>\n
- Use the degree of a polynomial\u00a0to determine the number of turning points of its graph<\/li>\n
- Draw the graph of a polynomial function using end behavior, turning points, intercepts, and the intermediate value theorem<\/li>\n
- Write the equation of a polynomial function given it’s graph<\/li>\n<\/ul>\n
\n- Use long division to divide polynomials.<\/li>\n
- Use synthetic division to divide polynomials.<\/li>\n<\/ul>\n
\n- Evaluate a polynomial using the Remainder Theorem.<\/li>\n
- Use the Factor Theorem to solve a polynomial equation.<\/li>\n
- Use the Rational Zero Theorem to find rational zeros.<\/li>\n
- Find zeros of a polynomial function.<\/li>\n
- Use the Linear Factorization Theorem to find polynomials with given zeros.<\/li>\n
- Use Descartes\u2019 Rule of Signs.<\/li>\n
- Solve real-world applications of polynomial equations<\/li>\n<\/ul>\n
Module 10: Rational and Radical Functions<\/h2>\n\n- Use arrow notation to describe end behavior of rational functions<\/li>\n
- Solve applied problems involving rational functions.<\/li>\n
- Find the domains of rational functions.<\/li>\n
- Identify vertical and horizontal asymptotes of graphs of rational functions<\/li>\n
- Graph rational functions.<\/li>\n
- Find the inverse of a polynomial function.<\/li>\n
- Restrict the domain to find the inverse of a polynomial function.<\/li>\n
- Solve direct variation problems.<\/li>\n
- Solve inverse variation problems.<\/li>\n
- Solve problems involving joint variation.<\/li>\n<\/ul>\n
Module 11:\u00a0Exponential and Logarithmic Functions<\/h2>\n\n- Evaluate an exponential growth function with different bases<\/li>\n
- Use a compound interest Formula<\/li>\n
- Write an exponential function<\/li>\n
- Find an exponential function given a graph<\/li>\n
- Use a graphing calculator to find an exponential function<\/li>\n
- Find an exponential function that models continuous growth or decay<\/li>\n
- Graph exponential functions, determine whether a graph represents exponential growth or decay<\/li>\n
- Graph exponential functions using transformations.<\/li>\n
- Convert from logarithmic to exponential form.<\/li>\n
- Convert from exponential to logarithmic form.<\/li>\n
- Evaluate common and natural logarithms.<\/li>\n
- Identify the domain of a logarithmic function.<\/li>\n
- Graph logarithmic functions using transformations, and identify intercepts and the vertical asymptote<\/li>\n
- Identify why and how a logarithmic function is an inverse of an exponential function<\/li>\n<\/ul>\n
Module 12:\u00a0Exponential and Logarithmic Equations and Models<\/h2>\n\n- Use power, product, and quotient rules to expand and condense logarithms<\/li>\n
- Use the change-of-base formula for logarithms.<\/li>\n
- Use like bases to solve exponential equations.<\/li>\n
- Use logarithms to solve exponential equations.<\/li>\n
- Use the definition of a logarithm to solve logarithmic equations.<\/li>\n
- Use the one-to-one property of logarithms to solve logarithmic equations.<\/li>\n
- Solve applied problems involving exponential and logarithmic equations.<\/li>\n
- Model exponential growth and decay.<\/li>\n
- Use Newton\u2019s Law of Cooling.<\/li>\n
- Use logistic-growth models.<\/li>\n
- Choose an appropriate model for data.<\/li>\n
- Express an exponential model in base e<\/em>.<\/li>\n
- Build an exponential model from data.<\/li>\n<\/ul>\n
Module 13:\u00a0Systems of Equations and Inequalities<\/h2>\n\n- Solve systems of equations by graphing,\u00a0substitution, and\u00a0addition.<\/li>\n
- Identify inconsistent systems of equations containing two variables.<\/li>\n
- Express the solution of a system of dependent equations containing two variables using standard notations.<\/li>\n<\/ul>\n
\n- Solve a system of nonlinear equations using substitution or elimination.<\/li>\n
- Graph a nonlinear inequality.<\/li>\n
- Graph a system of nonlinear inequalities.<\/li>\n<\/ul>\n
\n- Solve systems of three equations in three variables.<\/li>\n
- Identify inconsistent systems of equations containing three variables.<\/li>\n
- Express the solution of a system of dependent equations containing three variables using standard notations.<\/li>\n<\/ul>\n
\n- Decompose \u2009 [latex]\\frac{{P( x )}}{{ Q( x )}}[\/latex] ,\u2009 where \u2009Q( x )\u2009 has only nonrepeated linear factors.<\/li>\n
- Decompose \u2009[latex]\\frac{{P( x )}}{{ Q( x )}}[\/latex] ,\u2009 where \u2009Q( x )\u2009 has repeated linear factors.<\/li>\n
- Decompose \u2009[latex]\\frac{{P( x )}}{{ Q( x )}}[\/latex] ,\u2009 where \u2009Q( x )\u2009 has a nonrepeated irreducible quadratic factor.<\/li>\n
- Decompose \u2009[latex]\\frac{{P( x )}}{{ Q( x )}}[\/latex] ,\u2009 where \u2009Q( x )\u2009 has a repeated irreducible quadratic factor.<\/li>\n<\/ul>\n
Module 14: Solve Systems With Matrices<\/h2>\n\n- Find the sum and difference of two matrices.<\/li>\n
- Find scalar multiples of a matrix.<\/li>\n
- Find the product of two matrices.<\/li>\n
- Write the augmented matrix of a system of equations.<\/li>\n
- Write the system of equations from an augmented matrix.<\/li>\n
- Perform row operations on a matrix.<\/li>\n
- Solve a system of linear equations using matrices.<\/li>\n
- Find the inverse of a matrix.<\/li>\n
- Solve a system of linear equations using an inverse matrix.<\/li>\n<\/ul>\n
Module 15: Conic Sections<\/h2>\n\n- Write equations of ellipses in standard form<\/li>\n
- Graph ellipses centered at the origin<\/li>\n
- Graph ellipses not centered at the origin<\/li>\n
- Solve applied problems involving ellipses<\/li>\n
- Locate a hyperbola\u2019s vertices and foci<\/li>\n
- Write equations of hyperbolas in standard form<\/li>\n
- Graph hyperbolas centered at the origin<\/li>\n
- Graph hyperbolas not centered at the origin<\/li>\n
- Solve applied problems involving hyperbolas<\/li>\n
- Graph parabolas with vertices at the origin<\/li>\n
- Write equations of parabolas in standard form<\/li>\n
- Graph parabolas with vertices not at the origin<\/li>\n
- Solve applied problems involving parabolas<\/li>\n<\/ul>\n
Module 16:\u00a0Sequences and Series<\/h2>\n\n- Write the terms of a sequence defined by an explicit formula<\/li>\n
- Write the terms of a sequence defined by a recursive formula<\/li>\n
- Use factorial notation<\/li>\n
- Find the common difference for an arithmetic sequence<\/li>\n
- Write terms of an arithmetic sequence<\/li>\n
- Use a recursive formula for an arithmetic sequence<\/li>\n
- Use an explicit formula for an arithmetic sequence<\/li>\n
- Find the common ratio for a geometric sequence<\/li>\n
- List the terms of a geometric sequence<\/li>\n
- Use a recursive formula for a geometric sequence<\/li>\n
- Use an explicit formula for a geometric sequence<\/li>\n
- Use summation notation<\/li>\n
- Use the formula for the sum of the \ufb01rst [latex]n[\/latex] terms of an arithmetic series<\/li>\n
- Use the formula for the sum of the \ufb01rst [latex]n[\/latex] terms of a geometric series<\/li>\n
- Use the formula for the sum of an in\ufb01nite geometric series<\/li>\n
- Solve annuity problems<\/li>\n<\/ul>\n
Module 17: Probability and Counting Principles<\/h2>\n\n- Solve counting problems using the Addition Principle and the\u00a0Multiplication Principle<\/li>\n
- Solve counting problems using permutations and combinations \u00a0involving n distinct objects<\/li>\n
- Find the number of subsets of a given set<\/li>\n
- Solve counting problems using permutations involving n non-distinct objects<\/li>\n
- Apply the Binomial Theorem<\/li>\n
- Construct probability models<\/li>\n
- Compute probabilities of equally likely outcomes<\/li>\n
- Compute probabilities of the union of two events<\/li>\n
- Use the complement rule to find probabilities<\/li>\n
- Compute probability using counting theory<\/li>\n<\/ul>\n\n\t\t\t
\n\t\t\t Candela Citations<\/h3>\n\t\t\t\t\t \n\t\t\t\t\t\t \n\t\t\t\t\t\t\t CC licensed content, Original<\/div>- Learning Outcomes. Provided by<\/strong>: Lumen Learning. License<\/strong>: CC BY: Attribution<\/a><\/em><\/li><\/ul>CC licensed content, Shared previously<\/div>
- Magnify. Authored by<\/strong>: Eucalyp. Provided by<\/strong>: Noun Project. Located at<\/strong>: https:\/\/thenounproject.com\/term\/magnify\/1276779\/<\/a>. License<\/strong>: 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":17533,"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-4258","chapter","type-chapter","status-publish","hentry"],"part":4170,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/tulsacc-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/4258","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/tulsacc-collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/tulsacc-collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/tulsacc-collegealgebra\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":7,"href":"https:\/\/courses.lumenlearning.com\/tulsacc-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/4258\/revisions"}],"predecessor-version":[{"id":4802,"href":"https:\/\/courses.lumenlearning.com\/tulsacc-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/4258\/revisions\/4802"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/tulsacc-collegealgebra\/wp-json\/pressbooks\/v2\/parts\/4170"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/tulsacc-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/4258\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/tulsacc-collegealgebra\/wp-json\/wp\/v2\/media?parent=4258"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/tulsacc-collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=4258"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/tulsacc-collegealgebra\/wp-json\/wp\/v2\/contributor?post=4258"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/tulsacc-collegealgebra\/wp-json\/wp\/v2\/license?post=4258"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
- \r\n \t
- Classify a real number<\/li>\r\n \t
- Perform calculations using order of operations.<\/li>\r\n \t
- Use the properties of real numbers<\/li>\r\n \t
- Evaluate and simplify algebraic expressions.<\/li>\r\n \t
- Use the rules of exponents to simplify exponential expressions<\/li>\r\n \t
- Use scientific notation<\/li>\r\n \t
- Evaluate and simplify square roots<\/li>\r\n \t
- Rationalize a denominator that contains a square root<\/li>\r\n \t
- Rewrite a radical expression using rational exponents<\/li>\r\n<\/ul>\r\n
Module 2: Polynomial and Rational Expressions<\/h2>\r\n
- \r\n \t
- Identify the degree, leading coefficient, and leading term of a polynomial expression<\/li>\r\n \t
- Perform algebraic operations on polynomial expressions<\/li>\r\n \t
- Identify the greatest common factor of a polynomial expression<\/li>\r\n \t
- Factor a wide variety of polynomials including those with fractional or negative exponents<\/li>\r\n \t
- Simplify and perform algebraic operations on rational expressions<\/li>\r\n<\/ul>\r\n
Module 3: The Rectangular Coordinate System and Equations of Lines<\/h2>\r\n
- \r\n \t
- Plot ordered pairs, and graph equations by plotting points<\/li>\r\n \t
- Use a graphing utility to graph equations<\/li>\r\n \t
- Find the x and y intercepts of a graphed equation<\/li>\r\n \t
- Use the distance and midpoint formulas<\/li>\r\n \t
- Write equations of lines in slope-intercept, point-slope, and standard forms<\/li>\r\n \t
- Identify the equations and graphs of horizontal and vertical lines<\/li>\r\n \t
- Determine whether two lines are parallel, perpendicular, or neither<\/li>\r\n \t
- Write equations of lines that are parallel or perpendicular to another line<\/li>\r\n \t
- Develop a problem solving method<\/li>\r\n \t
- Write an equation to model an application<\/li>\r\n \t
- Solve distance, rate and time problems<\/li>\r\n \t
- Solve perimeter, area, and volume problems<\/li>\r\n<\/ul>\r\n
Module 4: Equations and Inequalities<\/h2>\r\n
- \r\n \t
- Solve equations involving rational exponents<\/li>\r\n \t
- Solve equations using factoring<\/li>\r\n \t
- Solve radical equations<\/li>\r\n \t
- Solve absolute value equations<\/li>\r\n \t
- Set up a linear equation to solve a real-world application<\/li>\r\n \t
- Use a formula to solve a real-world application<\/li>\r\n \t
- Solve quadratic equations by factoring<\/li>\r\n \t
- Solve quadratic equations by the square root property<\/li>\r\n \t
- Solve quadratic equations by completing the square<\/li>\r\n \t
- Solve quadratic equations by using the quadratic formula<\/li>\r\n \t
- Use interval notation<\/li>\r\n \t
- Use properties of inequalities<\/li>\r\n \t
- Solve inequalities in one variable algebraically<\/li>\r\n \t
- Solve absolute value inequalities<\/li>\r\n<\/ul>\r\n
Module 5: Function Basics<\/h2>\r\n
- \r\n \t
- Determine whether a relation represents a function<\/li>\r\n \t
- Find the value of a function<\/li>\r\n \t
- Determine whether a function is one-to-one<\/li>\r\n \t
- Use the vertical line test to identify functions<\/li>\r\n \t
- Graph the functions listed in the library of functions<\/li>\r\n \t
- Find the domain of a function defined by an equation<\/li>\r\n \t
- Write Domain and Range Using Standard Notations<\/li>\r\n \t
- Find Domain and Range from a Graph<\/li>\r\n \t
- Define Domain and Range of Toolkit Functions<\/li>\r\n \t
- Graph Piecewise-Defined Functions<\/li>\r\n \t
- Find the average rate of change of a function<\/li>\r\n \t
- Use a graph to determine where a function is increasing, decreasing, or constant<\/li>\r\n \t
- Use a graph to locate local maxima and local minima<\/li>\r\n \t
- Use a graph to locate the absolute maximum and absolute minimum<\/li>\r\n<\/ul>\r\n
Module 6:\u00a0Algebraic Operations on Functions<\/h2>\r\n
- \r\n \t
- Combine functions using algebraic operations<\/li>\r\n \t
- Create a new function by composition of functions<\/li>\r\n \t
- Evaluate composite functions<\/li>\r\n \t
- Find the domain of a composite function<\/li>\r\n \t
- Decompose a composite function into its component functions<\/li>\r\n \t
- Graph functions using vertical and horizontal shifts<\/li>\r\n \t
- Graph functions using reflections about the [latex]x[\/latex] -axis and the [latex]y[\/latex] -axis<\/li>\r\n \t
- Determine whether a function is even, odd, or neither from its graph<\/li>\r\n \t
- Graph functions using compressions and stretches<\/li>\r\n \t
- Combine transformations<\/li>\r\n \t
- Verify inverse functions<\/li>\r\n \t
- 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
- Find or evaluate the inverse of a function<\/li>\r\n \t
- Use the graph of a one-to-one function to graph its inverse function on the same axes<\/li>\r\n<\/ul>\r\n
Module 7: Linear and Absolute Value Functions<\/h2>\r\n
- \r\n \t
- Represent a linear function with an equation, words, a table and a graph<\/li>\r\n \t
- Determine whether a linear function is increasing, decreasing, or constant.<\/li>\r\n \t
- Write and interpret a linear function.<\/li>\r\n<\/ul>\r\n
- \r\n \t
- Graph linear functions by plotting points, using the slope and y-intercept, and by using transformations<\/li>\r\n \t
- 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
- Find the equations of vertical and horizontal lines<\/li>\r\n \t
- Graph an absolute value function, find it's intercepts<\/li>\r\n<\/ul>\r\n
- \r\n \t
- Identify steps for modeling and solving.<\/li>\r\n \t
- Build linear models from verbal descriptions.<\/li>\r\n \t
- Draw and interpret scatter plots.<\/li>\r\n \t
- Find the line of best fit using an online graphing tool.<\/li>\r\n \t
- Distinguish between linear and nonlinear relations.<\/li>\r\n \t
- Use a linear model to make predictions.<\/li>\r\n<\/ul>\r\n
Module 8:\u00a0Quadratic Functions<\/h2>\r\n
- \r\n \t
- Express square roots of negative numbers as multiples of\u2009i<\/li>\r\n \t
- Plot complex numbers on the complex plane<\/li>\r\n \t
- Add and subtract complex numbers<\/li>\r\n \t
- Multiply and divide complex numbers<\/li>\r\n<\/ul>\r\n
- \r\n \t
- Recognize characteristics of parabolas<\/li>\r\n \t
- Understand how the graph of a parabola is related to its quadratic function<\/li>\r\n<\/ul>\r\n
- \r\n \t
- Use the quadratic formula and factoring to find both real and complex roots (x-intercepts) of quadratic functions<\/li>\r\n \t
- Use algebra to find the y-intercepts of a quadratic function<\/li>\r\n \t
- Solve problems involving the roots and intercepts of a quadratic function<\/li>\r\n \t
- Use the discriminant to determine the nature (real or complex) and quantity of solutions to quadratic equations<\/li>\r\n \t
- Determine a quadratic function\u2019s minimum or maximum value<\/li>\r\n \t
- Solve problems involving a quadratic function\u2019s minimum or maximum value<\/li>\r\n<\/ul>\r\n
Module 9: Power and Polynomial Functions<\/h2>\r\n
- \r\n \t
- Identify power functions.<\/li>\r\n \t
- Identify end behavior of power functions.<\/li>\r\n \t
- Identify polynomial functions.<\/li>\r\n \t
- Identify the degree and leading coefficient of polynomial functions.<\/li>\r\n \t
- Identify local behavior of polynomial functions.<\/li>\r\n<\/ul>\r\n
- \r\n \t
- Identify zeros of polynomial functions with even and odd multiplicity<\/li>\r\n \t
- Use the degree of a polynomial\u00a0to determine the number of turning points of its graph<\/li>\r\n \t
- Draw the graph of a polynomial function using end behavior, turning points, intercepts, and the intermediate value theorem<\/li>\r\n \t
- Write the equation of a polynomial function given it's graph<\/li>\r\n<\/ul>\r\n
- \r\n \t
- Use long division to divide polynomials.<\/li>\r\n \t
- Use synthetic division to divide polynomials.<\/li>\r\n<\/ul>\r\n
- \r\n \t
- Evaluate a polynomial using the Remainder Theorem.<\/li>\r\n \t
- Use the Factor Theorem to solve a polynomial equation.<\/li>\r\n \t
- Use the Rational Zero Theorem to find rational zeros.<\/li>\r\n \t
- Find zeros of a polynomial function.<\/li>\r\n \t
- Use the Linear Factorization Theorem to find polynomials with given zeros.<\/li>\r\n \t
- Use Descartes\u2019 Rule of Signs.<\/li>\r\n \t
- Solve real-world applications of polynomial equations<\/li>\r\n<\/ul>\r\n
Module 10: Rational and Radical Functions<\/h2>\r\n
- \r\n \t
- Use arrow notation to describe end behavior of rational functions<\/li>\r\n \t
- Solve applied problems involving rational functions.<\/li>\r\n \t
- Find the domains of rational functions.<\/li>\r\n \t
- Identify vertical and horizontal asymptotes of graphs of rational functions<\/li>\r\n \t
- Graph rational functions.<\/li>\r\n \t
- Find the inverse of a polynomial function.<\/li>\r\n \t
- Restrict the domain to find the inverse of a polynomial function.<\/li>\r\n \t
- Solve direct variation problems.<\/li>\r\n \t
- Solve inverse variation problems.<\/li>\r\n \t
- Solve problems involving joint variation.<\/li>\r\n<\/ul>\r\n
Module 11:\u00a0Exponential and Logarithmic Functions<\/h2>\r\n
- \r\n \t
- Evaluate an exponential growth function with different bases<\/li>\r\n \t
- Use a compound interest Formula<\/li>\r\n \t
- Write an exponential function<\/li>\r\n \t
- Find an exponential function given a graph<\/li>\r\n \t
- Use a graphing calculator to find an exponential function<\/li>\r\n \t
- Find an exponential function that models continuous growth or decay<\/li>\r\n \t
- Graph exponential functions, determine whether a graph represents exponential growth or decay<\/li>\r\n \t
- Graph exponential functions using transformations.<\/li>\r\n \t
- Convert from logarithmic to exponential form.<\/li>\r\n \t
- Convert from exponential to logarithmic form.<\/li>\r\n \t
- Evaluate common and natural logarithms.<\/li>\r\n \t
- Identify the domain of a logarithmic function.<\/li>\r\n \t
- Graph logarithmic functions using transformations, and identify intercepts and the vertical asymptote<\/li>\r\n \t
- Identify why and how a logarithmic function is an inverse of an exponential function<\/li>\r\n<\/ul>\r\n
Module 12:\u00a0Exponential and Logarithmic Equations and Models<\/h2>\r\n
- \r\n \t
- Use power, product, and quotient rules to expand and condense logarithms<\/li>\r\n \t
- Use the change-of-base formula for logarithms.<\/li>\r\n \t
- Use like bases to solve exponential equations.<\/li>\r\n \t
- Use logarithms to solve exponential equations.<\/li>\r\n \t
- Use the definition of a logarithm to solve logarithmic equations.<\/li>\r\n \t
- Use the one-to-one property of logarithms to solve logarithmic equations.<\/li>\r\n \t
- Solve applied problems involving exponential and logarithmic equations.<\/li>\r\n \t
- Model exponential growth and decay.<\/li>\r\n \t
- Use Newton\u2019s Law of Cooling.<\/li>\r\n \t
- Use logistic-growth models.<\/li>\r\n \t
- Choose an appropriate model for data.<\/li>\r\n \t
- Express an exponential model in base e<\/em>.<\/li>\r\n \t
- Build an exponential model from data.<\/li>\r\n<\/ul>\r\n
Module 13:\u00a0Systems of Equations and Inequalities<\/h2>\r\n
- \r\n \t
- Solve systems of equations by graphing,\u00a0substitution, and\u00a0addition.<\/li>\r\n \t
- Identify inconsistent systems of equations containing two variables.<\/li>\r\n \t
- Express the solution of a system of dependent equations containing two variables using standard notations.<\/li>\r\n<\/ul>\r\n
- \r\n \t
- Solve a system of nonlinear equations using substitution or elimination.<\/li>\r\n \t
- Graph a nonlinear inequality.<\/li>\r\n \t
- Graph a system of nonlinear inequalities.<\/li>\r\n<\/ul>\r\n
- \r\n \t
- Solve systems of three equations in three variables.<\/li>\r\n \t
- Identify inconsistent systems of equations containing three variables.<\/li>\r\n \t
- Express the solution of a system of dependent equations containing three variables using standard notations.<\/li>\r\n<\/ul>\r\n
- \r\n \t
- Decompose \u2009 [latex]\\frac{{P( x )}}{{ Q( x )}}[\/latex] ,\u2009 where \u2009Q( x )\u2009 has only nonrepeated linear factors.<\/li>\r\n \t
- Decompose \u2009[latex]\\frac{{P( x )}}{{ Q( x )}}[\/latex] ,\u2009 where \u2009Q( x )\u2009 has repeated linear factors.<\/li>\r\n \t
- Decompose \u2009[latex]\\frac{{P( x )}}{{ Q( x )}}[\/latex] ,\u2009 where \u2009Q( x )\u2009 has a nonrepeated irreducible quadratic factor.<\/li>\r\n \t
- 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
Module 14: Solve Systems With Matrices<\/h2>\r\n
- \r\n \t
- Find the sum and difference of two matrices.<\/li>\r\n \t
- Find scalar multiples of a matrix.<\/li>\r\n \t
- Find the product of two matrices.<\/li>\r\n \t
- Write the augmented matrix of a system of equations.<\/li>\r\n \t
- Write the system of equations from an augmented matrix.<\/li>\r\n \t
- Perform row operations on a matrix.<\/li>\r\n \t
- Solve a system of linear equations using matrices.<\/li>\r\n \t
- Find the inverse of a matrix.<\/li>\r\n \t
- Solve a system of linear equations using an inverse matrix.<\/li>\r\n<\/ul>\r\n
Module 15: Conic Sections<\/h2>\r\n
- \r\n \t
- Write equations of ellipses in standard form<\/li>\r\n \t
- Graph ellipses centered at the origin<\/li>\r\n \t
- Graph ellipses not centered at the origin<\/li>\r\n \t
- Solve applied problems involving ellipses<\/li>\r\n \t
- Locate a hyperbola\u2019s vertices and foci<\/li>\r\n \t
- Write equations of hyperbolas in standard form<\/li>\r\n \t
- Graph hyperbolas centered at the origin<\/li>\r\n \t
- Graph hyperbolas not centered at the origin<\/li>\r\n \t
- Solve applied problems involving hyperbolas<\/li>\r\n \t
- Graph parabolas with vertices at the origin<\/li>\r\n \t
- Write equations of parabolas in standard form<\/li>\r\n \t
- Graph parabolas with vertices not at the origin<\/li>\r\n \t
- Solve applied problems involving parabolas<\/li>\r\n<\/ul>\r\n
Module 16:\u00a0Sequences and Series<\/h2>\r\n
- \r\n \t
- Write the terms of a sequence defined by an explicit formula<\/li>\r\n \t
- Write the terms of a sequence defined by a recursive formula<\/li>\r\n \t
- Use factorial notation<\/li>\r\n \t
- Find the common difference for an arithmetic sequence<\/li>\r\n \t
- Write terms of an arithmetic sequence<\/li>\r\n \t
- Use a recursive formula for an arithmetic sequence<\/li>\r\n \t
- Use an explicit formula for an arithmetic sequence<\/li>\r\n \t
- Find the common ratio for a geometric sequence<\/li>\r\n \t
- List the terms of a geometric sequence<\/li>\r\n \t
- Use a recursive formula for a geometric sequence<\/li>\r\n \t
- Use an explicit formula for a geometric sequence<\/li>\r\n \t
- Use summation notation<\/li>\r\n \t
- Use the formula for the sum of the \ufb01rst [latex]n[\/latex] terms of an arithmetic series<\/li>\r\n \t
- Use the formula for the sum of the \ufb01rst [latex]n[\/latex] terms of a geometric series<\/li>\r\n \t
- Use the formula for the sum of an in\ufb01nite geometric series<\/li>\r\n \t
- Solve annuity problems<\/li>\r\n<\/ul>\r\n
Module 17: Probability and Counting Principles<\/h2>\r\n
- \r\n \t
- Solve counting problems using the Addition Principle and the\u00a0Multiplication Principle<\/li>\r\n \t
- Solve counting problems using permutations and combinations \u00a0involving n distinct objects<\/li>\r\n \t
- Find the number of subsets of a given set<\/li>\r\n \t
- Solve counting problems using permutations involving n non-distinct objects<\/li>\r\n \t
- Apply the Binomial Theorem<\/li>\r\n \t
- Construct probability models<\/li>\r\n \t
- Compute probabilities of equally likely outcomes<\/li>\r\n \t
- Compute probabilities of the union of two events<\/li>\r\n \t
- Use the complement rule to find probabilities<\/li>\r\n \t
- Compute probability using counting theory<\/li>\r\n<\/ul>","rendered":"<\/p>\n
The content, assignments, and assessments for College Algebra are aligned to the following learning outcomes. A full list of course learning outcomes can be viewed here: College Algebra Learning Outcomes.<\/a><\/p>\n
Module 1: Algebra Essentials<\/h2>\n
Evaluate and simplify expressions that contain both real numbers and variables<\/h3>\n
- \n
- Classify a real number<\/li>\n
- Perform calculations using order of operations.<\/li>\n
- Use the properties of real numbers<\/li>\n
- Evaluate and simplify algebraic expressions.<\/li>\n
- Use the rules of exponents to simplify exponential expressions<\/li>\n
- Use scientific notation<\/li>\n
- Evaluate and simplify square roots<\/li>\n
- Rationalize a denominator that contains a square root<\/li>\n
- Rewrite a radical expression using rational exponents<\/li>\n<\/ul>\n
Module 2: Polynomial and Rational Expressions<\/h2>\n
- \n
- Identify the degree, leading coefficient, and leading term of a polynomial expression<\/li>\n
- Perform algebraic operations on polynomial expressions<\/li>\n
- Identify the greatest common factor of a polynomial expression<\/li>\n
- Factor a wide variety of polynomials including those with fractional or negative exponents<\/li>\n
- Simplify and perform algebraic operations on rational expressions<\/li>\n<\/ul>\n
Module 3: The Rectangular Coordinate System and Equations of Lines<\/h2>\n
- \n
- Plot ordered pairs, and graph equations by plotting points<\/li>\n
- Use a graphing utility to graph equations<\/li>\n
- Find the x and y intercepts of a graphed equation<\/li>\n
- Use the distance and midpoint formulas<\/li>\n
- Write equations of lines in slope-intercept, point-slope, and standard forms<\/li>\n
- Identify the equations and graphs of horizontal and vertical lines<\/li>\n
- Determine whether two lines are parallel, perpendicular, or neither<\/li>\n
- Write equations of lines that are parallel or perpendicular to another line<\/li>\n
- Develop a problem solving method<\/li>\n
- Write an equation to model an application<\/li>\n
- Solve distance, rate and time problems<\/li>\n
- Solve perimeter, area, and volume problems<\/li>\n<\/ul>\n
Module 4: Equations and Inequalities<\/h2>\n
- \n
- Solve equations involving rational exponents<\/li>\n
- Solve equations using factoring<\/li>\n
- Solve radical equations<\/li>\n
- Solve absolute value equations<\/li>\n
- Set up a linear equation to solve a real-world application<\/li>\n
- Use a formula to solve a real-world application<\/li>\n
- Solve quadratic equations by factoring<\/li>\n
- Solve quadratic equations by the square root property<\/li>\n
- Solve quadratic equations by completing the square<\/li>\n
- Solve quadratic equations by using the quadratic formula<\/li>\n
- Use interval notation<\/li>\n
- Use properties of inequalities<\/li>\n
- Solve inequalities in one variable algebraically<\/li>\n
- Solve absolute value inequalities<\/li>\n<\/ul>\n
Module 5: Function Basics<\/h2>\n
- \n
- Determine whether a relation represents a function<\/li>\n
- Find the value of a function<\/li>\n
- Determine whether a function is one-to-one<\/li>\n
- Use the vertical line test to identify functions<\/li>\n
- Graph the functions listed in the library of functions<\/li>\n
- Find the domain of a function defined by an equation<\/li>\n
- Write Domain and Range Using Standard Notations<\/li>\n
- Find Domain and Range from a Graph<\/li>\n
- Define Domain and Range of Toolkit Functions<\/li>\n
- Graph Piecewise-Defined Functions<\/li>\n
- Find the average rate of change of a function<\/li>\n
- Use a graph to determine where a function is increasing, decreasing, or constant<\/li>\n
- Use a graph to locate local maxima and local minima<\/li>\n
- Use a graph to locate the absolute maximum and absolute minimum<\/li>\n<\/ul>\n
Module 6:\u00a0Algebraic Operations on Functions<\/h2>\n
- \n
- Combine functions using algebraic operations<\/li>\n
- Create a new function by composition of functions<\/li>\n
- Evaluate composite functions<\/li>\n
- Find the domain of a composite function<\/li>\n
- Decompose a composite function into its component functions<\/li>\n
- Graph functions using vertical and horizontal shifts<\/li>\n
- Graph functions using reflections about the [latex]x[\/latex] -axis and the [latex]y[\/latex] -axis<\/li>\n
- Determine whether a function is even, odd, or neither from its graph<\/li>\n
- Graph functions using compressions and stretches<\/li>\n
- Combine transformations<\/li>\n
- Verify inverse functions<\/li>\n
- Determine the domain and range of an inverse function, and restrict the domain of a function to make it one-to-one<\/li>\n
- Find or evaluate the inverse of a function<\/li>\n
- Use the graph of a one-to-one function to graph its inverse function on the same axes<\/li>\n<\/ul>\n
Module 7: Linear and Absolute Value Functions<\/h2>\n
- \n
- Represent a linear function with an equation, words, a table and a graph<\/li>\n
- Determine whether a linear function is increasing, decreasing, or constant.<\/li>\n
- Write and interpret a linear function.<\/li>\n<\/ul>\n
- \n
- Graph linear functions by plotting points, using the slope and y-intercept, and by using transformations<\/li>\n
- Write the equation of a linear function given it’s graph, including vertical and horizontal lines, match linear equations with their graphs<\/li>\n
- Find the equations of vertical and horizontal lines<\/li>\n
- Graph an absolute value function, find it’s intercepts<\/li>\n<\/ul>\n
- \n
- Identify steps for modeling and solving.<\/li>\n
- Build linear models from verbal descriptions.<\/li>\n
- Draw and interpret scatter plots.<\/li>\n
- Find the line of best fit using an online graphing tool.<\/li>\n
- Distinguish between linear and nonlinear relations.<\/li>\n
- Use a linear model to make predictions.<\/li>\n<\/ul>\n
Module 8:\u00a0Quadratic Functions<\/h2>\n
- \n
- Express square roots of negative numbers as multiples of\u2009i<\/li>\n
- Plot complex numbers on the complex plane<\/li>\n
- Add and subtract complex numbers<\/li>\n
- Multiply and divide complex numbers<\/li>\n<\/ul>\n
- \n
- Recognize characteristics of parabolas<\/li>\n
- Understand how the graph of a parabola is related to its quadratic function<\/li>\n<\/ul>\n
- \n
- Use the quadratic formula and factoring to find both real and complex roots (x-intercepts) of quadratic functions<\/li>\n
- Use algebra to find the y-intercepts of a quadratic function<\/li>\n
- Solve problems involving the roots and intercepts of a quadratic function<\/li>\n
- Use the discriminant to determine the nature (real or complex) and quantity of solutions to quadratic equations<\/li>\n
- Determine a quadratic function\u2019s minimum or maximum value<\/li>\n
- Solve problems involving a quadratic function\u2019s minimum or maximum value<\/li>\n<\/ul>\n
Module 9: Power and Polynomial Functions<\/h2>\n
- \n
- Identify power functions.<\/li>\n
- Identify end behavior of power functions.<\/li>\n
- Identify polynomial functions.<\/li>\n
- Identify the degree and leading coefficient of polynomial functions.<\/li>\n
- Identify local behavior of polynomial functions.<\/li>\n<\/ul>\n
- \n
- Identify zeros of polynomial functions with even and odd multiplicity<\/li>\n
- Use the degree of a polynomial\u00a0to determine the number of turning points of its graph<\/li>\n
- Draw the graph of a polynomial function using end behavior, turning points, intercepts, and the intermediate value theorem<\/li>\n
- Write the equation of a polynomial function given it’s graph<\/li>\n<\/ul>\n
- \n
- Use long division to divide polynomials.<\/li>\n
- Use synthetic division to divide polynomials.<\/li>\n<\/ul>\n
- \n
- Evaluate a polynomial using the Remainder Theorem.<\/li>\n
- Use the Factor Theorem to solve a polynomial equation.<\/li>\n
- Use the Rational Zero Theorem to find rational zeros.<\/li>\n
- Find zeros of a polynomial function.<\/li>\n
- Use the Linear Factorization Theorem to find polynomials with given zeros.<\/li>\n
- Use Descartes\u2019 Rule of Signs.<\/li>\n
- Solve real-world applications of polynomial equations<\/li>\n<\/ul>\n
Module 10: Rational and Radical Functions<\/h2>\n
- \n
- Use arrow notation to describe end behavior of rational functions<\/li>\n
- Solve applied problems involving rational functions.<\/li>\n
- Find the domains of rational functions.<\/li>\n
- Identify vertical and horizontal asymptotes of graphs of rational functions<\/li>\n
- Graph rational functions.<\/li>\n
- Find the inverse of a polynomial function.<\/li>\n
- Restrict the domain to find the inverse of a polynomial function.<\/li>\n
- Solve direct variation problems.<\/li>\n
- Solve inverse variation problems.<\/li>\n
- Solve problems involving joint variation.<\/li>\n<\/ul>\n
Module 11:\u00a0Exponential and Logarithmic Functions<\/h2>\n
- \n
- Evaluate an exponential growth function with different bases<\/li>\n
- Use a compound interest Formula<\/li>\n
- Write an exponential function<\/li>\n
- Find an exponential function given a graph<\/li>\n
- Use a graphing calculator to find an exponential function<\/li>\n
- Find an exponential function that models continuous growth or decay<\/li>\n
- Graph exponential functions, determine whether a graph represents exponential growth or decay<\/li>\n
- Graph exponential functions using transformations.<\/li>\n
- Convert from logarithmic to exponential form.<\/li>\n
- Convert from exponential to logarithmic form.<\/li>\n
- Evaluate common and natural logarithms.<\/li>\n
- Identify the domain of a logarithmic function.<\/li>\n
- Graph logarithmic functions using transformations, and identify intercepts and the vertical asymptote<\/li>\n
- Identify why and how a logarithmic function is an inverse of an exponential function<\/li>\n<\/ul>\n
Module 12:\u00a0Exponential and Logarithmic Equations and Models<\/h2>\n
- \n
- Use power, product, and quotient rules to expand and condense logarithms<\/li>\n
- Use the change-of-base formula for logarithms.<\/li>\n
- Use like bases to solve exponential equations.<\/li>\n
- Use logarithms to solve exponential equations.<\/li>\n
- Use the definition of a logarithm to solve logarithmic equations.<\/li>\n
- Use the one-to-one property of logarithms to solve logarithmic equations.<\/li>\n
- Solve applied problems involving exponential and logarithmic equations.<\/li>\n
- Model exponential growth and decay.<\/li>\n
- Use Newton\u2019s Law of Cooling.<\/li>\n
- Use logistic-growth models.<\/li>\n
- Choose an appropriate model for data.<\/li>\n
- Express an exponential model in base e<\/em>.<\/li>\n
- Build an exponential model from data.<\/li>\n<\/ul>\n
Module 13:\u00a0Systems of Equations and Inequalities<\/h2>\n
- \n
- Solve systems of equations by graphing,\u00a0substitution, and\u00a0addition.<\/li>\n
- Identify inconsistent systems of equations containing two variables.<\/li>\n
- Express the solution of a system of dependent equations containing two variables using standard notations.<\/li>\n<\/ul>\n
- \n
- Solve a system of nonlinear equations using substitution or elimination.<\/li>\n
- Graph a nonlinear inequality.<\/li>\n
- Graph a system of nonlinear inequalities.<\/li>\n<\/ul>\n
- \n
- Solve systems of three equations in three variables.<\/li>\n
- Identify inconsistent systems of equations containing three variables.<\/li>\n
- Express the solution of a system of dependent equations containing three variables using standard notations.<\/li>\n<\/ul>\n
- \n
- Decompose \u2009 [latex]\\frac{{P( x )}}{{ Q( x )}}[\/latex] ,\u2009 where \u2009Q( x )\u2009 has only nonrepeated linear factors.<\/li>\n
- Decompose \u2009[latex]\\frac{{P( x )}}{{ Q( x )}}[\/latex] ,\u2009 where \u2009Q( x )\u2009 has repeated linear factors.<\/li>\n
- Decompose \u2009[latex]\\frac{{P( x )}}{{ Q( x )}}[\/latex] ,\u2009 where \u2009Q( x )\u2009 has a nonrepeated irreducible quadratic factor.<\/li>\n
- Decompose \u2009[latex]\\frac{{P( x )}}{{ Q( x )}}[\/latex] ,\u2009 where \u2009Q( x )\u2009 has a repeated irreducible quadratic factor.<\/li>\n<\/ul>\n
Module 14: Solve Systems With Matrices<\/h2>\n
- \n
- Find the sum and difference of two matrices.<\/li>\n
- Find scalar multiples of a matrix.<\/li>\n
- Find the product of two matrices.<\/li>\n
- Write the augmented matrix of a system of equations.<\/li>\n
- Write the system of equations from an augmented matrix.<\/li>\n
- Perform row operations on a matrix.<\/li>\n
- Solve a system of linear equations using matrices.<\/li>\n
- Find the inverse of a matrix.<\/li>\n
- Solve a system of linear equations using an inverse matrix.<\/li>\n<\/ul>\n
Module 15: Conic Sections<\/h2>\n
- \n
- Write equations of ellipses in standard form<\/li>\n
- Graph ellipses centered at the origin<\/li>\n
- Graph ellipses not centered at the origin<\/li>\n
- Solve applied problems involving ellipses<\/li>\n
- Locate a hyperbola\u2019s vertices and foci<\/li>\n
- Write equations of hyperbolas in standard form<\/li>\n
- Graph hyperbolas centered at the origin<\/li>\n
- Graph hyperbolas not centered at the origin<\/li>\n
- Solve applied problems involving hyperbolas<\/li>\n
- Graph parabolas with vertices at the origin<\/li>\n
- Write equations of parabolas in standard form<\/li>\n
- Graph parabolas with vertices not at the origin<\/li>\n
- Solve applied problems involving parabolas<\/li>\n<\/ul>\n
Module 16:\u00a0Sequences and Series<\/h2>\n
- \n
- Write the terms of a sequence defined by an explicit formula<\/li>\n
- Write the terms of a sequence defined by a recursive formula<\/li>\n
- Use factorial notation<\/li>\n
- Find the common difference for an arithmetic sequence<\/li>\n
- Write terms of an arithmetic sequence<\/li>\n
- Use a recursive formula for an arithmetic sequence<\/li>\n
- Use an explicit formula for an arithmetic sequence<\/li>\n
- Find the common ratio for a geometric sequence<\/li>\n
- List the terms of a geometric sequence<\/li>\n
- Use a recursive formula for a geometric sequence<\/li>\n
- Use an explicit formula for a geometric sequence<\/li>\n
- Use summation notation<\/li>\n
- Use the formula for the sum of the \ufb01rst [latex]n[\/latex] terms of an arithmetic series<\/li>\n
- Use the formula for the sum of the \ufb01rst [latex]n[\/latex] terms of a geometric series<\/li>\n
- Use the formula for the sum of an in\ufb01nite geometric series<\/li>\n
- Solve annuity problems<\/li>\n<\/ul>\n
Module 17: Probability and Counting Principles<\/h2>\n
- \n
- Solve counting problems using the Addition Principle and the\u00a0Multiplication Principle<\/li>\n
- Solve counting problems using permutations and combinations \u00a0involving n distinct objects<\/li>\n
- Find the number of subsets of a given set<\/li>\n
- Solve counting problems using permutations involving n non-distinct objects<\/li>\n
- Apply the Binomial Theorem<\/li>\n
- Construct probability models<\/li>\n
- Compute probabilities of equally likely outcomes<\/li>\n
- Compute probabilities of the union of two events<\/li>\n
- Use the complement rule to find probabilities<\/li>\n
- Compute probability using counting theory<\/li>\n<\/ul>\n\n\t\t\t
\n\t\t\t Candela Citations<\/h3>\n\t\t\t\t\t
\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tCC licensed content, Original<\/div>- Learning Outcomes. Provided by<\/strong>: Lumen Learning. License<\/strong>: CC BY: Attribution<\/a><\/em><\/li><\/ul>CC licensed content, Shared previously<\/div>
- Magnify. Authored by<\/strong>: Eucalyp. Provided by<\/strong>: Noun Project. Located at<\/strong>: https:\/\/thenounproject.com\/term\/magnify\/1276779\/<\/a>. License<\/strong>: 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":17533,"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-4258","chapter","type-chapter","status-publish","hentry"],"part":4170,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/tulsacc-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/4258","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/tulsacc-collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/tulsacc-collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/tulsacc-collegealgebra\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":7,"href":"https:\/\/courses.lumenlearning.com\/tulsacc-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/4258\/revisions"}],"predecessor-version":[{"id":4802,"href":"https:\/\/courses.lumenlearning.com\/tulsacc-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/4258\/revisions\/4802"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/tulsacc-collegealgebra\/wp-json\/pressbooks\/v2\/parts\/4170"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/tulsacc-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/4258\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/tulsacc-collegealgebra\/wp-json\/wp\/v2\/media?parent=4258"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/tulsacc-collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=4258"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/tulsacc-collegealgebra\/wp-json\/wp\/v2\/contributor?post=4258"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/tulsacc-collegealgebra\/wp-json\/wp\/v2\/license?post=4258"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
- Learning Outcomes. Provided by<\/strong>: Lumen Learning. License<\/strong>: CC BY: Attribution<\/a><\/em><\/li><\/ul>
- Build an exponential model from data.<\/li>\n<\/ul>\n
- Build an exponential model from data.<\/li>\r\n<\/ul>\r\n