Contents

Preface

1 Review of Basic Algebra

1.1 The Real Number System

1.2 The Real Number Line

1.3 Integer Exponents

1.4 Radicals

1.5 Rational Exponents

1.6 Polynomials and Special Products

1.7 Factoring Polynomials

1.8 Rational Expressions

Chapter 1 Review Exercises

2 Equations and Inequalities

2.1 Equations

2.2 Building an Equation from Words

2.3 Quadratic Equations

2.4 Complex Numbers

2.5 Linear Inequalities

2.6 Absolute-Value Equations and Inequalities

2.7 Polynomial and Rational Inequalities

Chapter 2 Review Exercises

3 Rectangular Coordinate System and Graphs

3.1 The Rectangular Coordinate System

3.2 Circles and Graphs

3.3 Equations of Lines

3.4 Variation

Chapter 3 Review Exercises

4 Functions and Graphs

4.1 Functions and Graphs

4.2 Symmetry and Transformations

4.3 Linear and Quadratic Functions

4.4 Piecewise-Defined Functions

4.5 Combining Functions

4.6 Inverse Functions

4.7 Building a Function from Words

4.8 Least Squares Line

Chapter 4 Review Exercises

5 Polynomial and Rational Functions

5.1 Polynomial Functions

5.2 Division of Polynomial Functions

5.3 Zeros and Factors of Polynomial Functions

5.4 Real Zeros of Polynomial Functions

5.5 Approximating Real Zeros

5.6 Rational Functions

Chapter 5 Review Exercises

6 Exponential and Logarithmic Functions

6.1 Exponential Functions

6.2 Logarithmic Functions

6.3 Exponential and Logarithmic Equations

6.4 Exponential and Logarithmic Models

6.5 Hyperbolic Functions

Chapter 6 Review Exercises

7 Topics in Analytic Geometry

7.1 The Parabola

7.2 The Ellipse

7.3 The Hyperbola

Chapter 7 Review Exercises

8 Systems of Equations and Inequalities

8.1 Systems of Linear Equations

8.2 Systems of Nonlinear Equations

8.3 Partial Fractions

8.4 Systems of Inequalities

8.5 Linear Programming

Chapter 8 Review Exercises

9 Matrices and Determinants

9.1 Introduction to Matrices

9.2 Algebra of Matrices

9.3 Determinants

9.4 Inverse of a Matrix

9.5 Linear Systems: Augmented Matrices

9.6 Linear Systems: Matrix Inverses

9.7 Linear Systems: Determinants

9.8 Cryptography

Chapter 9 Review Exercises

10 Sequences, Series, and Probability

10.1 Sequences

10.2 Series

10.3 Convergence of Sequences and Series

10.4 Mathematical Induction

10.5 The Binomial Theorem

10.6 Principles of Counting

10.7 Introduction to Probability

Chapter 10 Review Exercises

Answers to Selected Odd-Numbered Problems

Index

Credits