## Table of Contents

Preface

Acknowledgments

To the Student

About the Author

Applications Index

**P. Prerequisites: Fundamental Concepts of Algebra**

P.1 Algebraic Expressions, Mathematical Models, and Real Numbers

P.2 Basic Rules of Algebra

P.3 Exponents and Scientific Notation

P.4 Radicals and Rational Exponents

P.5 Polynomials

Mid-Chapter Check Point

P.6 Factoring Polynomials

P.7 Rational Expressions

Summary, Review, and Test

Review Exercises

Chapter P Test

**1. Functions and Graphs**

1.1 Graphs and Graphing Utilities

1.2 Basics of Functions and Their Graphs

1.3 More on Functions and Their Graphs

1.4 Linear Functions and Slope

1.5 More on Slope

Mid-Chapter Check Point

1.6 Transformations of Functions

1.7 Combinations of Functions; Composite Functions

1.8 Inverse Functions

1.9 Distance and Midpoint Formulas; Circles

Summary, Review, and Test

Review Exercises

Chapter 1 Test

**2. Equations and Inequalities**

2.1 Linear Equations and Rational Equations

2.2 Models and Applications

2.3 Complex Numbers

2.4 Quadratic Equations

Mid-Chapter Check Point

2.5 Other Types of Equations

2.6 Linear Inequalities and Absolute Value Inequalities

Summary, Review, and Test

Review Exercises

Chapter 2 Test

Cumulative Review Exercises (Chapters 1-2)

**3. Polynomial and Rational Functions**

3.1 Quadratic Functions

3.2 Polynomial Functions and Their Graphs

3.3 Dividing Polynomials; Remainder and Factor Theorems

3.4 Zeros of Polynomial Functions

Mid-Chapter Check Point

3.5 Rational Functions and Their Graphs

3.6 Polynomial and Rational Inequalities

3.7 Modeling Using Variation

Summary, Review, and Test

Review Exercises

Chapter 3 Test

Cumulative Review Exercises (Chapters 1-3)

**4. Exponential and Logarithmic Functions**

4.1 Exponential Functions

4.2 Logarithmic Functions

4.3 Properties of Logarithms

Mid-Chapter Check Point

4.4 Exponential and Logarithmic Equations

4.5 Exponential Growth and Decay; Modeling Data

Summary, Review, and Test

Review Exercises

Chapter 4 Test

Cumulative Review Exercises (Chapters 1-4)

**5. Systems of Equations and Inequalities**

5.1 Systems of Linear Equations in Two Variables

5.2 Systems of Linear Equations in Three Variables

5.3 Partial Fractions

5.4 Systems of Nonlinear Equations in Two Variables

Mid-Chapter Check Point

5.5 Systems of Inequalities

5.6 Linear Programming

Summary, Review, and Test

Review Exercises

Chapter 5 Test

Cumulative Review Exercises (Chapters 1-5)

**6. Matrices and Determinants**

6.1 Matrix Solutions to Linear Systems

6.2 Inconsistent and Dependent Systems and Their Applications

6.3 Matrix Operations and Their Applications

Mid-Chapter Check Point

6.4 Multiplicative Inverses of Matrices and Matrix Equations

6.5 Determinants and Cramer's Rule

Summary, Review, and Test

Review Exercises

Chapter 6 Test

Cumulative Review Exercises (Chapters 1-6)

**7. Conic Sections**

7.1 The Ellipse

7.2 The Hyperbola

Mid-Chapter Check Point

7.3 The Parabola

Summary, Review, and Test

Review Exercises

Chapter 7 Test

Cumulative Review Exercises (Chapters 1-7)

**8. Sequences, Induction, and Probability**

8.1 Sequences and Summation Notation

8.2 Arithmetic Sequences

8.3 Geometric Sequences and Series

Mid-Chapter Check Point

8.4 Mathematical Induction

8.5 The Binomial Theorem

8.6 Counting Principles, Permutations, and Combinations

8.7 Probability

Summary, Review, And Test

Review Exercises

Chapter 8 Test

Cumulative Review Exercises (Chapters 1-8)

Appendix: Where Did That Come From? Selected Proofs

Answers to Selected Exercises

Subject Index

Photo Credits