Functions and Function Notation

Use arrow notation

Introduction to Functions and Function Notation

Solve applied problems involving rational functions

Determine whether a relation represents a function

Find the domains of rational functions

Find the input and output values of a function

Identify vertical asymptotes

Determine whether a function is one-to-one

Identify horizontal asymptotes

Use the vertical line test to identify functions

Graph rational functions

Graph the functions listed in the library of functions

Key Concepts & Glossary

Key Concepts & Glossary

Section Exercises

Section Exercises

Solutions

Solutions

Inverses and Radical Functions

Domain and Range

Introduction to Inverses and Radical Functions

Introduction to Domain and Range

Find the inverse of a polynomial function

Find the domain of a function defined by an equation

Restrict the domain to find the inverse of a polynomial function

Use notations to specify domain and range

Key Concepts & Glossary

Find domain and range from graphs

Section Exercises

Find domains and ranges of the toolkit functions

Solutions

Graph piecewise-defined functions

Modeling Using Variation

Key Concepts & Glossary

Introduction to Modeling Using Variation

Section Exercises

Solve direct variation problems

Solutions

Solve inverse variation problems

Rates of Change and Behavior of Graphs

Solve problems involving joint variation

Introduction to Rates of Change and Behaviors of Graphs

Key Concepts & Glossary

Find the average rate of change of a function

Section Exercises

Use a graph to determine where a function is increasing, decreasing, or constant

Solutions

Use a graph to locate the absolute maximum and absolute minimum

Exponential Functions

Key Concepts & Glossary

Introduction to Exponential Functions

Section Exercises

Evaluate exponential functions

Solutions

Find the equation of an exponential function

Composition of Functions

Use compound interest formulas

Introduction to Composition of Functions

Evaluate exponential functions with base e

Combine functions using algebraic operations

Key Concepts & Glossary

Create a new function by composition of functions

Section Exercises

Evaluate composite functions

Solutions

Find the domain of a composite function

Graphs of Exponential Functions

Decompose a composite function into its component functions

Introduction to Graphs of Exponential Functions

Key Concepts & Glossary

Graph exponential functions

Section Exercises

Graph exponential functions using transformations

Solutions

Key Concepts

Transformation of Functions

Section Exercises

Introduction to Transformation of Functions

Solutions

Graph functions using vertical and horizontal shifts

Logarithmic Functions

Graph functions using reflections about the x-axis and the y-axis

Introduction to Logarithmic Functions

Determine whether a function is even, odd, or neither from its graph

Convert from logarithmic to exponential form

Graph functions using compressions and stretches

Convert from exponential to logarithmic form

Combine vertical and horizontal shifts

Evaluate logarithms

Key Concepts & Glossary

Use common logarithms

Section Exercises

Use natural logarithms

Solutions

Key Concepts & Glossary

Absolute Value Functions

Section Exercises

Introduction to Absolute Value Functions

Solutions

Graph an absolute value function

Graphs of Logarithmic Functions

Solve an absolute value equation

Introduction to Graphs of Logarithmic Functions

Solve an absolute value inequality

Identify the domain of a logarithmic function

Key Concepts & Glossary

Graph logarithmic functions

Section Exercises

Graphing Transformations of Logarithmic Functions

Solutions

Key Concepts

Inverse Functions

Section Exercises

Introduction to Inverse Functions

Solutions

Verify inverse functions

Logarithmic Properties

Determine the domain and range of an inverse function

Introduction to Logarithmic Properties

Find or evaluate the inverse of a function

Use the product rule for logarithms

Use the graph of a function to graph its inverse

Use the quotient and power rules for logarithms

Key Concepts & Glossary

Expand logarithmic expressions

Section Exercises

Condense logarithmic expressions

Solutions

Use the change-of-base formula for logarithms

Linear Functions

Key Terms & Glossary

Introduction to Linear Functions

Section Exercises

Represent a linear function

Solutions

Determine whether a linear function is increasing, decreasing, or constant

Exponential and Logarithmic Equations

Calculate and interpret slope

Introduction to Exponential and Logarithmic Equations

Write the point-slope form of an equation

Use like bases to solve exponential equations

Write and interpret a linear function

Use logarithms to solve exponential equations

Key Concepts & Glossary

Use the definition of a logarithm to solve logarithmic equations

Section Exercises

Use the one-to-one property of logarithms to solve logarithmic equations

Solutions

Solve applied problems involving exponential and logarithmic equations

Graphs of Linear Functions

Key Concepts & Glossary

Introduction to Graphs of Linear Functions

Section Exercises

Graph linear functions

Solutions

Write the equation for a linear function from the graph of a line

Fitting Exponential Models to Data

Given the equations of two lines, determine whether their graphs are parallel or perpendicular

Introduction to Fitting Exponential Models to Data

Write the equation of a line parallel or perpendicular to a given line

Build an exponential model from data

Solve a system of linear equations

Build a logarithmic model from data

Key Concepts & Glossary

Build a logistic model from data

Section Exercises

Key Concepts

Solutions

Section Exercises

Modeling with Linear Functions

Solutions

Introduction to Modeling With Linear Functions

Exponential and Logarithmic Models

Identify steps for modeling and solving

Introduction to Exponential and Logarithmic Models

Build linear models

Model exponential growth and decay

Build systems of linear models

Use Newton’s Law of Cooling

Section Exercises

Use logistic-growth models

Solutions

Choose an appropriate model for data

Fitting Linear Models to Data

Key Concepts & Glossary

Introduction to Fitting Linear Models to Data

Section Exercises

Draw and interpret scatter plots

Solutions

Find the line of best fit

Systems of Linear Equations: Two Variables

Distinguish between linear and nonlinear relations

Introduction to Systems of Linear Equations: Two Variables

Use a linear model to make predictions

Solving Systems of Equations by Graphing

Key Concepts & Glossary

Solving Systems of Equations by Substitution

Section Exercises

Solving Systems of Equations in Two Variables by the Addition Method

Solutions

Identifying and Expressing Solutions to Systems of Equations

Complex Numbers

Using Systems of Equations to Investigate Profits

Introduction to Complex Numbers

Key Concepts & Glossary

Express square roots of negative numbers as multiples of  i

Section Exercises

Plot complex numbers on the complex plane

Solutions

Add and subtract complex numbers

Systems of Linear Equations: Three Variables

Multiply and divide complex numbers

Introduction to Systems of Linear Equations: Three Variables

Key Concepts & Glossary

Solving Systems of Three Equations in Three Variables

Section Exercises

Inconsistent and Dependent Systems in Three Variables

Solutions

Key Concepts & Glossary

Quadratic Functions

Section Exercises

Introduction to Quadratic Functions

Solutions

Recognize characteristics of parabolas

Systems of Nonlinear Equations and Inequalities: Two Variables

Understand how the graph of a parabola is related to its quadratic function

Introduction to Systems of Nonlinear Equations and Inequalities: Two Variables

Determine a quadratic function’s minimum or maximum value

Solving a System of Nonlinear Equations Using Substitution

Solve problems involving a quadratic function’s minimum or maximum value

Solving a System of Nonlinear Equations Using Elimination

Key Concepts & Glossary

Graphing Nonlinear Inequalities and Systems of Nonlinear Inequalities

Section Exercises

Key Concepts & Glossary

Solutions

Section Exercises

Power Functions and Polynomial Functions

Solutions

Introduction to Power Functions and Polynomial Functions

Matrices and Matrix Operations

Identify power functions

Introduction: Matrices and Matrix Operations

Identify end behavior of power functions

Finding the Sum and Difference of Two Matrices

Identify polynomial functions

Finding Scalar Multiples of a Matrix

Identify the degree and leading coefficient of polynomial functions

Finding the Product of Two Matrices

Key Concepts & Glossary

Key Concepts & Glossary

Section Exercises

Section Exercises

Solutions

Solutions

Graphs of Polynomial Functions

Solving Systems with Gaussian Elimination

Introduction to Graphs of Polynomial Functions

Introduction to Solving Systems with Gaussian Elimination

Recognize characteristics of graphs of polynomial functions

The Augmented Matrix of a System of Equations

Use factoring to find zeros of polynomial functions

Performing Row Operations on a Matrix

Identify zeros and their multiplicities

Solving a System of Linear Equations Using Matrices

Determine end behavior

Key Concepts & Glossary

Understand the relationship between degree and turning points

Section Exercises

Graph polynomial functions

Solutions

Use the Intermediate Value Theorem

Solving Systems with Inverses

Key Concepts & Glossary

Introduction to Solving Systems with Inverses

Section Exercises

Finding the Inverse of a Matrix

Solutions

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

Dividing Polynomials

Key Concepts & Glossary

Introduction to Dividing Polynomials

Section Exercises

Use long division to divide polynomials

Solutions

Use synthetic division to divide polynomials

Solving Systems with Cramer's Rule

Use polynomial division to solve application problems

Introduction to Solving Systems with Cramer's Rule

Key Concepts & Glossary

Using Cramer’s Rule to Solve a System of Two Equations in Two Variables

Section Exercises

Using Cramer’s Rule to Solve a System of Three Equations in Three Variables

Solutions

Understanding Properties of Determinants

Zeros of Polynomial Functions

Key Concepts & Glossary

Introduction to Zeros of Polynomials

Solutions

Evaluate a polynomial using the Remainder Theorem**

Section Exercises

Use the Factor Theorem to solve a polynomial equation

Practice Tests

Use the Rational Zero Theorem to find rational zeros

Functions Practice Test

Find zeros of a polynomial function

Solutions: Functions Practice Test

Use the Fundamental Theorem of Algebra

Linear Functions Practice Test

Use the Linear Factorization Theorem to find polynomials with given zeros

Solutions: Linear Functions Practice Test

Use Descartes’ Rule of Signs

Polynomial and Rational Functions Practice Test

Solve real-world applications of polynomial equations

Solutions: Polynomial and Rational Functions Practice Test

Key Concepts & Glossary

Exponential and Logarithmic Functions Practice Test

Section Exercises

Solutions: Exponential and Logarithmic Functions Practice Test

Solutions

Appendix

Rational Functions

Appendix

Introduction to Rational Functions