## Table of Contents

Preface

To the Student

Just-In-Time Review

**1. Graphs, Functions, and Models**

1.1 Introduction to Graphing

Visualizing the Graph

1.2 Functions and Graphs

1.3 Linear Functions, Slope, and Applications

Visualizing the Graph

Mid-Chapter Mixed Review

1.4 Equations of Lines and Modeling

1.5 Linear Equations, Functions, Zeros, and Applications

1.6 Solving Linear Inequalities

Study Guide

Review Exercises

Test

**2. More on Functions**

2.1 Increasing, Decreasing, and Piecewise Functions; Applications

2.2 The Algebra of Functions

2.3 The Composition of Functions

Mid-Chapter Mixed Review

2.4 Symmetry

2.5 Transformations

Visualizing the Graph

2.6 Variation and Application

Study Guide

Review Exercises

Test

**3. Quadratic Functions and Equations; Inequalities**

3.1 The Complex Numbers

3.2 Quadratic Equations, Functions, Zeros, and Models

3.3 Analyzing Graphs of Quadratic Functions

Visualizing the Graph

Mid-Chapter Review

3.4 Solving Rational Equations and Radical Equations

3.5 Solving Equations and Inequalities with Absolute Value

Study Guide

Review Exercises

Test

**4. Polynomial Functions and Rational Functions**

4.1 Polynomial Functions and Modeling

4.2 Graphing Polynomial Functions

Visualizing the Graph

4.3 Polynomial Division; The Remainder Theorem and the Factor Theorem

Mid-Chapter Mixed Review

4.4 Theorems about Zeros of Polynomial Functions

4.5 Rational Functions

Visualizing the Graph

4.6 Polynomial Inequalities and Rational Inequalities

Study Guide

Review Exercises

Test

**5. Exponential Functions and Logarithmic Functions**

5.1 Inverse Functions

5.2 Exponential Functions and Graphs

5.3 Logarithmic Functions and Graphs

Visualizing the Graph

Mid-Chapter Mixed Review

5.4 Properties of Logarithmic Functions

5.5 Solving Exponential Equations and Logarithmic Equations

5.6 Applications and Models: Growth and Decay; Compound Interest

Study Guide

Review Exercises

Test

**6. The Trigonometric Functions**

6.1 Trigonometric Functions of Acute Angles

6.2 Applications of Right Triangles

6.3 Trigonometric Functions of Any Angle

Mid-Chapter Mixed Review

6.4 Radians, Arc Length, and Angular Speed

6.5 Circular Functions: Graphs and Properties

6.6 Graphs of Transformed Sine Functions and Cosine Functions

Visualizing the Graph

Study Guide

Review Exercises

Test

**7. Trigonometric Identities, Inverse Functions, and Equations**

7.1 Identities: Pythagorean and Sum and Difference

7.2 Identities: Cofunction, Double-Angle, and Half-Angle

7.3 Proving Trigonometric Identities

Mid-Chapter Mixed Review

7.4 Inverses of the Trigonometric Functions

7.5 Solving Trigonometric Equations

Visualizing the Graph

Study Guide

Review Exercises

Test

**8. Applications of Trigonometry**

8.1 The Law of Sines

8.2 The Law of Cosines

8.3 Complex Numbers: Trigonometric Notation

Mid-Chapter Mixed Review

8.4 Polar Coordinates and Graphs

Visualizing the Graph

8.5 Vectors and Applications

8.6 Vector Operations

Study Guide

Review Exercises

Test

**9. Systems of Equations and Matrices**

9.1 Systems of Equations in Two Variables

Visualizing the Graph

9.2 Systems of Equations in Three Variables

9.3 Matrices and Systems of Equations

9.4 Matrix Operations

Mid-Chapter Mixed Review

9.5 Inverses of Matrices

9.6 Determinants and Cramer’s Rule

9.7 Systems of Inequalities and Linear Programming

6.8 Partial Fractions

Study Guide

Review Exercises

Test

**10. Analytic Geometry Topics**

10.1 The Parabola

10.2 The Circle and the Ellipse

10.3 The Hyperbola

10.4 Nonlinear Systems of Equations and Inequalities

Visualizing the Graph

Mid-Chapter Mixed Review

10.5 Rotation of Axes

10.6 Polar Equations of Conics

10.7 Parametric Equations

Study Guide

Review Exercises

Test

**11. Sequences, Series, and Combinatorics**

11.1 Sequences and Series

11.2 Arithmetic Sequences and Series

11.3 Geometric Sequences and Series

Visualizing the Graph

11.4 Mathematical Induction

Mid-Chapter Mixed Review

11.5 Combinatorics: Permutations

11.6 Combinatorics: Combinations

11.7 The Binomial Theorem

11.8 Probability

Study Guide

Review Exercises

Test

Photo Credits

Answers // Additional Instructor’s Answers

Index

Index of Applications