The following list shows a summary of the topics covered in this course. To see all of the course pages, visit the Table of Contents.

## Module 1: Functions and Function Notation

- Determine whether a relation represents a function
- Find the input and output values 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

## Module 2: Domain and Range

- Find the domain of a function defined by an equation
- Use notations to specify domain and range
- Find domain and range from graphs
- Find domains and ranges of the toolkit functions
- Graph piecewise-defined functions

**Module 3: **Rates of Change and Behavior of Graphs

- 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 the absolute maximum and absolute minimum

**Module 4: **Composition of 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

**Module 5: **Transformation of Functions

- Graph functions using vertical and horizontal shifts
- Graph functions using reflections about the x-axis and the y-axis
- Determine whether a function is even, odd, or neither from its graph
- Graph functions using compressions and stretches
- Combine vertical and horizontal shifts

**Module 6: **Absolute Value Functions

- Graph an absolute value function
- Solve an absolute value equation
- Solve an absolute value inequality

**Module 7: **Inverse Functions

- Verify inverse functions
- Determine the domain and range of an inverse function
- Find or evaluate the inverse of a function
- Use the graph of a function to graph its inverse

**Module 8: **Linear Functions

- Represent a linear function
- Determine whether a linear function is increasing, decreasing, or constant
- Calculate and interpret slope
- Write the point-slope form of an equation
- Write and interpret a linear function

**Module 9: **Graphs of Linear Functions

- Graph linear functions
- Write the equation for a linear function from the graph of a line
- Given the equations of two lines, determine whether their graphs are parallel or perpendicular
- Write the equation of a line parallel or perpendicular to a given line
- Solve a system of linear equations

**Module 10: **Modeling with Linear Functions

- Identify steps for modeling and solving
- Build linear models
- Build systems of linear models

**Module 11: **Fitting Linear Models to Data

- Draw and interpret scatter plots
- Find the line of best fit
- Distinguish between linear and nonlinear relations
- Use a linear model to make predictions

**Module 12: **Complex Numbers

- 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

**Module 13: **Quadratic Functions

- Recognize characteristics of parabolas
- Understand how the graph of a parabola is related to its quadratic function
- Determine a quadratic function’s minimum or maximum value
- Solve problems involving a quadratic function’s minimum or maximum value

**Module 14: **Power Functions and Polynomial Functions

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

**Module 15: **Graphs of Polynomial Functions

- Recognize characteristics of graphs of polynomial functions
- Use factoring to ﬁnd zeros of polynomial functions
- Identify zeros and their multiplicities
- Determine end behavior
- Understand the relationship between degree and turning points
- Graph polynomial functions
- Solving Polynomial Inequalities
- Use the Intermediate Value Theorem

**Module 16: **Dividing Polynomials

- Use long division to divide polynomials
- Use synthetic division to divide polynomials
- Use polynomial division to solve application problems

**Module 17: **Zeros of Polynomial Functions

- 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 Fundamental Theorem of Algebra
- Use the Linear Factorization Theorem to find polynomials with given zeros
- Use Descartes’ Rule of Signs
- Solve real-world applications of polynomial equations

**Module 18: **Rational Functions

- Use arrow notation
- Solve applied problems involving rational functions
- Find the domains of rational functions
- Identify vertical asymptotes
- Identify horizontal asymptotes
- Graph rational functions

**Module 19: **Inverses and Radical Functions

- Find the inverse of a polynomial function
- Restrict the domain to find the inverse of a polynomial function

**Module 20: **Modeling Using Variation

- Solve direct variation problems
- Solve inverse variation problems
- Solve problems involving joint variation

**Module 21: **Exponential Functions

- Evaluate exponential functions
- Find the equation of an exponential function
- Use compound interest formulas
- Evaluate exponential functions with base e

**Module 22: **Graphs of Exponential Functions

- Graph exponential functions
- Graph exponential functions using transformations

**Module 23: **Logarithmic Functions

- Convert from logarithmic to exponential form
- Convert from exponential to logarithmic form
- Evaluate logarithms
- Use common logarithms
- Use natural logarithms

**Module 24: **Graphs of Logarithmic Functions

- Identify the domain of a logarithmic function
- Graph logarithmic functions
- Graphing Transformations of Logarithmic Functions

**Module 25: **Logarithmic Properties

- Use the product rule for logarithms
- Use the quotient and power rules for logarithms
- Expand logarithmic expressions
- Condense logarithmic expressions
- Use the change-of-base formula for logarithms

**Module 26: **Exponential and Logarithmic Equations

- 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

**Module 27: **Exponential and Logarithmic Models

- Model exponential growth and decay
- Use Newton’s Law of Cooling
- Use logistic-growth models
- Choose an appropriate model for data

**Module 28: **Fitting Exponential Models to Data

- Build an exponential model from data
- Build a logarithmic model from data
- Build a logistic model from data

**Module 29: **Systems of Linear Equations: Two Variables

- Solving Systems of Equations by Graphing
- Solving Systems of Equations by Substitution
- Solving Systems of Equations in Two Variables by the Addition Method
- Identifying and Expressing Solutions to Systems of Equations
- Using Systems of Equations to Investigate Profits

**Module 30: **Systems of Linear Equations: Three Variables

- Solving Systems of Three Equations in Three Variables
- Inconsistent and Dependent Systems in Three Variables

**Module 31: **Matrices and Matrix Operations

- Finding the Sum and Difference of Two Matrices
- Finding Scalar Multiples of a Matrix
- Finding the Product of Two Matrices

**Module 32: **Solving Systems with Gaussian Elimination

- The Augmented Matrix of a System of Equations
- Performing Row Operations on a Matrix
- Solving a System of Linear Equations Using Matrices

**Module 33: **Solving Systems with Inverses

- Finding the Inverse of a Matrix
- Solving a System of Linear Equations Using the Inverse of a Matrix

**Module 34: **Sequences and Their Notations

- Writing the Terms of a Sequence Defined by an Explicit Formula
- Investigating Alternating Sequences
- Investigating Explicit Formulas
- Writing the Terms of a Sequence Defined by a Recursive Formula

**Module 35: **Arithmetic Sequences

- Finding Common Differences
- Using Formulas for Arithmetic Sequences
- Finding the Number of Terms in a Finite Arithmetic Sequence

**Module 36: **Geometric Sequences

- Finding Common Ratios
- Writing Terms of Geometric Sequences
- Solving Application Problems with Geometric Sequences

**Module 37: **Series and Their Notations

- Using Summation Notation
- Using the Formula for Arithmetic Series
- Using the Formula for Geometric Series
- Finding Sums of Infinite Series
- Solving Annuity Problems