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.

## Module 1: Algebra Essentials

### Evaluate and simplify expressions that contain both real numbers and variables

- Classify a real number
- Perform calculations using order of operations.
- Use the properties of real numbers
- Evaluate and simplify algebraic expressions.
- Use the rules of exponents to simplify exponential expressions
- Use scientific notation
- Evaluate and simplify square roots
- Rationalize a denominator that contains a square root
- Rewrite a radical expression using rational exponents

## Module 2: Polynomial and Rational Expressions

- Identify the degree, leading coefficient, and leading term of a polynomial expression
- Perform algebraic operations on polynomial expressions
- Identify the greatest common factor of a polynomial expression
- Factor a wide variety of polynomials including those with fractional or negative exponents
- Simplify and perform algebraic operations on rational expressions

## Module 3: The Rectangular Coordinate System and Equations of Lines

- Plot ordered pairs, and graph equations by plotting points
- Use a graphing utility to graph equations
- Find the x and y intercepts of a graphed equation
- Use the distance and midpoint formulas
- Write equations of lines in slope-intercept, point-slope, and standard forms
- Identify the equations and graphs of horizontal and vertical lines
- Determine whether two lines are parallel, perpendicular, or neither
- Write equations of lines that are parallel or perpendicular to another line
- Develop a problem solving method
- Write an equation to model an application
- Solve distance, rate and time problems
- Solve perimeter, area, and volume problems

## Module 4: Equations and Inequalities

- Solve equations involving rational exponents
- Solve equations using factoring
- Solve radical equations
- Solve absolute value equations
- Set up a linear equation to solve a real-world application
- Use a formula to solve a real-world application
- Solve quadratic equations by factoring
- Solve quadratic equations by the square root property
- Solve quadratic equations by completing the square
- Solve quadratic equations by using the quadratic formula
- Use interval notation
- Use properties of inequalities
- Solve inequalities in one variable algebraically
- Solve absolute value inequalities

## Module 5: Function Basics

- Determine whether a relation represents a function
- Find the value of a function
- Determine whether a function is one-to-one
- Use the vertical line test to identify functions
- Graph the functions listed in the library of functions
- Find the domain of a function defined by an equation
- Write Domain and Range Using Standard Notations
- Find Domain and Range from a Graph
- Define Domain and Range of Toolkit Functions
- Graph Piecewise-Defined Functions
- Find the average rate of change of a function
- Use a graph to determine where a function is increasing, decreasing, or constant
- Use a graph to locate local maxima and local minima
- Use a graph to locate the absolute maximum and absolute minimum

## Module 6: Algebraic Operations on Functions

- Combine functions using algebraic operations
- Create a new function by composition of functions
- Evaluate composite functions
- Find the domain of a composite function
- Decompose a composite function into its component functions
- Graph functions using vertical and horizontal shifts
- Graph functions using reflections about the [latex]x[/latex] -axis and the [latex]y[/latex] -axis
- Determine whether a function is even, odd, or neither from its graph
- Graph functions using compressions and stretches
- Combine transformations
- Verify inverse functions
- Determine the domain and range of an inverse function, and restrict the domain of a function to make it one-to-one
- Find or evaluate the inverse of a function
- Use the graph of a one-to-one function to graph its inverse function on the same axes

## Module 7: Linear and Absolute Value Functions

- Represent a linear function with an equation, words, a table and a graph
- Determine whether a linear function is increasing, decreasing, or constant.
- Write and interpret a linear function.

- Graph linear functions by plotting points, using the slope and y-intercept, and by using transformations
- Write the equation of a linear function given it’s graph, including vertical and horizontal lines, match linear equations with their graphs
- Find the equations of vertical and horizontal lines
- Graph an absolute value function, find it’s intercepts

- Identify steps for modeling and solving.
- Build linear models from verbal descriptions.
- Draw and interpret scatter plots.
- Find the line of best fit using an online graphing tool.
- Distinguish between linear and nonlinear relations.
- Use a linear model to make predictions.

## Module 8: Quadratic Functions

- Express square roots of negative numbers as multiples of i
- Plot complex numbers on the complex plane
- Add and subtract complex numbers
- Multiply and divide complex numbers

- Recognize characteristics of parabolas
- Understand how the graph of a parabola is related to its quadratic function

- Use the quadratic formula and factoring to find both real and complex roots (x-intercepts) of quadratic functions
- Use algebra to find the y-intercepts of a quadratic function
- Solve problems involving the roots and intercepts of a quadratic function
- Use the discriminant to determine the nature (real or complex) and quantity of solutions to quadratic equations
- Determine a quadratic function’s minimum or maximum value
- Solve problems involving a quadratic function’s minimum or maximum value

## Module 9: Power and Polynomial Functions

- Identify power functions.
- Identify end behavior of power functions.
- Identify polynomial functions.
- Identify the degree and leading coefficient of polynomial functions.
- Identify local behavior of polynomial functions.

- Identify zeros of polynomial functions with even and odd multiplicity
- Use the degree of a polynomial to determine the number of turning points of its graph
- Draw the graph of a polynomial function using end behavior, turning points, intercepts, and the intermediate value theorem
- Write the equation of a polynomial function given it’s graph

- Use long division to divide polynomials.
- Use synthetic division to divide polynomials.

- Evaluate a polynomial using the Remainder Theorem.
- Use the Factor Theorem to solve a polynomial equation.
- Use the Rational Zero Theorem to find rational zeros.
- Find zeros of a polynomial function.
- Use the Linear Factorization Theorem to find polynomials with given zeros.
- Use Descartes’ Rule of Signs.
- Solve real-world applications of polynomial equations

## Module 10: Rational and Radical Functions

- Use arrow notation to describe end behavior of rational functions
- Solve applied problems involving rational functions.
- Find the domains of rational functions.
- Identify vertical and horizontal asymptotes of graphs of rational functions
- Graph rational functions.
- Find the inverse of a polynomial function.
- Restrict the domain to find the inverse of a polynomial function.
- Solve direct variation problems.
- Solve inverse variation problems.
- Solve problems involving joint variation.

## Module 11: Exponential and Logarithmic Functions

- Evaluate an exponential growth function with different bases
- Use a compound interest Formula
- Write an exponential function
- Find an exponential function given a graph
- Use a graphing calculator to find an exponential function
- Find an exponential function that models continuous growth or decay
- Graph exponential functions, determine whether a graph represents exponential growth or decay
- Graph exponential functions using transformations.
- Convert from logarithmic to exponential form.
- Convert from exponential to logarithmic form.
- Evaluate common and natural logarithms.
- Identify the domain of a logarithmic function.
- Graph logarithmic functions using transformations, and identify intercepts and the vertical asymptote
- Identify why and how a logarithmic function is an inverse of an exponential function

## Module 12: Exponential and Logarithmic Equations and Models

- Use power, product, and quotient rules to expand and condense logarithms
- Use the change-of-base formula for logarithms.
- Use like bases to solve exponential equations.
- Use logarithms to solve exponential equations.
- Use the definition of a logarithm to solve logarithmic equations.
- Use the one-to-one property of logarithms to solve logarithmic equations.
- Solve applied problems involving exponential and logarithmic equations.
- Model exponential growth and decay.
- Use Newton’s Law of Cooling.
- Use logistic-growth models.
- Choose an appropriate model for data.
- Express an exponential model in base
*e*. - Build an exponential model from data.

## Module 13: Systems of Equations and Inequalities

- Solve systems of equations by graphing, substitution, and addition.
- Identify inconsistent systems of equations containing two variables.
- Express the solution of a system of dependent equations containing two variables using standard notations.

- Solve a system of nonlinear equations using substitution or elimination.
- Graph a nonlinear inequality.
- Graph a system of nonlinear inequalities.

- Solve systems of three equations in three variables.
- Identify inconsistent systems of equations containing three variables.
- Express the solution of a system of dependent equations containing three variables using standard notations.

- Decompose [latex]\frac{{P( x )}}{{ Q( x )}}[/latex] , where Q( x ) has only nonrepeated linear factors.
- Decompose [latex]\frac{{P( x )}}{{ Q( x )}}[/latex] , where Q( x ) has repeated linear factors.
- Decompose [latex]\frac{{P( x )}}{{ Q( x )}}[/latex] , where Q( x ) has a nonrepeated irreducible quadratic factor.
- Decompose [latex]\frac{{P( x )}}{{ Q( x )}}[/latex] , where Q( x ) has a repeated irreducible quadratic factor.

## Module 14: Solve Systems With Matrices

- Find the sum and difference of two matrices.
- Find scalar multiples of a matrix.
- Find the product of two matrices.
- Write the augmented matrix of a system of equations.
- Write the system of equations from an augmented matrix.
- Perform row operations on a matrix.
- Solve a system of linear equations using matrices.
- Find the inverse of a matrix.
- Solve a system of linear equations using an inverse matrix.

## Module 15: Conic Sections

- Write equations of ellipses in standard form
- Graph ellipses centered at the origin
- Graph ellipses not centered at the origin
- Solve applied problems involving ellipses
- Locate a hyperbola’s vertices and foci
- Write equations of hyperbolas in standard form
- Graph hyperbolas centered at the origin
- Graph hyperbolas not centered at the origin
- Solve applied problems involving hyperbolas
- Graph parabolas with vertices at the origin
- Write equations of parabolas in standard form
- Graph parabolas with vertices not at the origin
- Solve applied problems involving parabolas

## Module 16: Sequences and Series

- Write the terms of a sequence defined by an explicit formula
- Write the terms of a sequence defined by a recursive formula
- Use factorial notation
- Find the common difference for an arithmetic sequence
- Write terms of an arithmetic sequence
- Use a recursive formula for an arithmetic sequence
- Use an explicit formula for an arithmetic sequence
- Find the common ratio for a geometric sequence
- List the terms of a geometric sequence
- Use a recursive formula for a geometric sequence
- Use an explicit formula for a geometric sequence
- Use summation notation
- Use the formula for the sum of the ﬁrst [latex]n[/latex] terms of an arithmetic series
- Use the formula for the sum of the ﬁrst [latex]n[/latex] terms of a geometric series
- Use the formula for the sum of an inﬁnite geometric series
- Solve annuity problems

## Module 17: Probability and Counting Principles

- Solve counting problems using the Addition Principle and the Multiplication Principle
- Solve counting problems using permutations and combinations involving n distinct objects
- Find the number of subsets of a given set
- Solve counting problems using permutations involving n non-distinct objects
- Apply the Binomial Theorem
- Construct probability models
- Compute probabilities of equally likely outcomes
- Compute probabilities of the union of two events
- Use the complement rule to find probabilities
- Compute probability using counting theory