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Table of Contents

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PREFACE

APPLICATIONS INDEX

Chapter 1: The Real Numbers

1.1 Sets

1.2 The Real Numbers

1.3 Operations on the Set of Real Numbers

1.4 Evaluating Expressions and the Order of Operations

1.5 Properties of the Real Numbers

1.6 Using the Properties

Chapter 2: Linear Equations and Inequalities in One Variable

2.1 Linear Equations in One Variable

2.2 Formulas and Functions

2.3 Applications

2.4 Inequalities

2.5 Compound Inequalities

2.6 Absolute Value Equations and Inequalities

Chapter 3: Linear Equations and Inequalities in Two Variables

3.1 Graphing Lines in the Coordinate Plane

3.2 Slope of a Line

3.3 Three Forms for the Equation of a Line

3.4 Linear Inequalities and Their Graphs

3.5 Functions and Relations

Chapter 4: Systems of Linear Equations

4.1 Solving Systems by Graphing and Substitution

4.2 The Addition Method

4.3 Systems of Linear Equations in Three Variables

4.4 Solving Linear Systems Using Matrices

4.5 Determinants and Cramer’s Rule

4.6 Linear Programming

Chapter 5: Exponents and Polynomials

5.1 Integral Exponents and Scientific Notation

5.2 The Power Rules

5.3 Polynomials and Polynomial Functions

5.4 Multiplying Binomials

5.5 Factoring Polynomials

5.6 Factoring ax² + bx + c

5.7 Factoring Strategy

5.8 Solving Equations by Factoring

Chapter 6: Rational Expressions and Functions

6.1 Properties of Rational Expressions and Functions

6.2 Multiplication and Division

6.3 Addition and Subtraction

6.4 Complex Fractions

6.5 Division of Polynomials

6.6 Solving Equations Involving Rational Expressions

6.7 Applications

Chapter 7: Radicals and Rational Exponents

7.1 Radicals

7.2 Rational Exponents

7.3 Adding, Subtracting, and Multiplying Radicals

7.4 Quotients, Powers, and Rationalizing Denominators

7.5 Solving Equations with Radicals and Exponents

7.6 Complex Numbers

Chapter 8: Quadratic Equations, Functions, and Inequalities

8.1 Factoring and Completing the Square

8.2 The Quadratic Formula

8.3 More on Quadratic Equations

8.4 Quadratic Functions and Their Graphs

8.5 Quadratic Inequalities

Chapter 9: Additional Function Topics

9.1 Graphs of Functions and Relations

9.2 Transformations of Graphs

9.3 Combining Functions

9.4 Inverse Functions

9.5 Variation

Chapter 10: Polynomial and Rational Functions

10.1 The Factor Theorem

10.2 Zeros of a Polynomial Function

10.3 The Theory of Equations

10.4 Graphs of Polynomial Functions

10.5 Graphs of Rational Functions

Chapter 11: Exponential and Logarithmic Functions

11.1 Exponential Functions and Their Applications

11.2 Logarithmic Functions and Their Applications

11.3 Properties of Logarithms

11.4 Solving Equations and Applications

Chapter 12: Nonlinear Systems and the Conic Sections

12.1 Nonlinear Systems of Equations

12.2 The Parabola

12.3 The Circle

12.4 The Ellipse and Hyperbola

12.5 Second-Degree Inequalities

Chapter 13: Sequences and Series

13.1 Sequences

13.2 Series

13.3 Arithmetic Sequences and Series

13.4 Geometric Sequences and Series

13.5 Binomial Expansions

Chapter 14: Counting and Probability

14.1 Counting and Permutations

14.2 Combinations

14.3 Probability

Appendix A

Answers to Selected Exercises

Index