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Table of Contents
PREFACE APPLICATIONS INDEX 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 1 Wrap-Up • Summary • Enriching Your Mathematical Word Power • Review Exercises • Chapter 1 Test • Critical Thinking 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 2 Wrap-Up • Summary • Enriching Your Mathematical Word Power • Review Exercises • Chapter 2 Test • Making Connections: A review of Chapters 1-2 • Critical Thinking 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 3 Wrap-Up • Summary • Enriching Your Mathematical Word Power • Review Exercises • Chapter 3 Test • Making Connections: a review of Chapters 1-3 • Critical Thinking 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 4 Wrap-Up • Summary • Enriching Your Mathematical Word Power • Review Exercises • Chapter 4 Test • Making Connections: a review of Chapters 1-4 • Critical Thinking 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 5 Wrap-Up • Summary • Enriching Your Mathematical Word Power • Review Exercises • Chapter 5 Test • Making Connections: a review of Chapters 1-5 • Critical Thinking 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 6 Wrap-Up • Summary • Enriching Your Mathematical Word Power • Review Exercises • Chapter 6 Test • Making Connections: a review of Chapters 1-6 • Critical Thinking 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 7 Wrap-Up • Summary • Enriching Your Mathematical Word Power • Review Exercises • Chapter 7 Test • Making Connections: a review of Chapters 1-7 • Critical Thinking 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 8 Wrap-Up • Summary • Enriching Your Mathematical Word Power • Review Exercises • Chapter 8 Test • Making Connections: a review of Chapters 1-8 • Critical Thinking 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 9 Wrap-Up • Summary • Enriching Your Mathematical Word Power • Review Exercises • Chapter 9 Test • Making Connections: a review of Chapters 1-9 • Critical Thinking 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 10 Wrap-Up • Summary • Enriching Your Mathematical Word Power • Review Exercises • Chapter 10 Test • Making Connections: a review of Chapters 1-10 • Critical Thinking 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 11 Wrap-Up • Summary • Enriching Your Mathematical Word Power • Review Exercises • Chapter 11 Test • Making Connections: a review of Chapters 1-11 • Critical Thinking 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 12 Wrap-Up • Summary • Enriching Your Mathematical Word Power • Review Exercises • Chapter 12 Test • Making Connections: a review of Chapters 1-12 • Critical Thinking 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 13 Wrap-Up • Summary • Enriching Your Mathematical Word Power • Review Exercises • Chapter 13 Test • Making Connections: a review of Chapters 1-13 • Critical Thinking 14 Counting and Probability 14.1 Counting and Permutations 14.2 Combinations 14.3 Probability Chapter 14 Wrap-Up • Summary • Enriching Your Mathematical Word Power • Review Exercises • Chapter 14 Test • Critical Thinking Appendix A Answers to Selected Exercises Index