Contents. The Real Numbers. Linear Equations and Inequalities in One Variable

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1 dug33513_fm.qxd 11/20/07 3:21 PM Page vii Preface Guided Tour: Features and Supplements Applications Index 1 2 The Real Numbers Sets 2 The Real Numbers 9 Operations on the Set of Real Numbers 19 Evaluating Expressions 30 Properties of the Real Numbers 40 Using the Properties 48 Chapter 1 Wrap-Up 56 Summary 56 Enriching Your Mathematical Word Power 58 Review Exercises 59 Chapter 1 Test 62 Critical Thinking 64 Linear Equations and Inequalities in One Variable xiii xix xxx 65 Linear Equations in One Variable 66 Formulas and Functions 78 Applications 89 Inequalities 102 Compound Inequalities 114 Absolute Value Equations and Inequalities 125 Chapter 2 Wrap-Up 135 Summary 135 Enriching Your Mathematical Word Power 137 Review Exercises 137 Chapter 2 Test 142 Making Connections: A Review of Chapters Critical Thinking 144 vii

2 dug33513_fm.qxd 11/20/07 3:21 PM Page viii viii Linear Equations and Inequalities in Two Variables Graphing Lines in the Coordinate Plane 146 Slope of a Line 158 Three Forms for the Equation of a Line 170 Linear Inequalities and Their Graphs 183 Functions and Relations 199 Chapter 3 Wrap-Up 211 Summary 211 Enriching Your Mathematical Word Power 214 Review Exercises 215 Chapter 3 Test 220 Making Connections: A Review of Chapters Critical Thinking 224 Systems of Linear Equations Solving Systems by Graphing and Substitution 226 The Addition Method 238 Systems of Linear Equations in Three Variables 247 Solving Linear Systems Using Matrices 255 Determinants and Cramer s Rule 264 Linear Programming 275 Chapter 4 Wrap-Up 282 Summary 282 Enriching Your Mathematical Word Power 284 Review Exercises 285 Chapter 4 Test 288 Making Connections: A Review of Chapters Critical Thinking 290 Exponents and Polynomials Integral Exponents and Scientific Notation 292 The Power Rules 305 Polynomials and Polynomial Functions 314 Multiplying Binomials 323 Factoring Polynomials 331 Factoring ax2 bx c 341 Factoring Strategy

3 dug33513_fm.qxd 11/20/07 3:22 PM Page ix Solving Equations by Factoring 358 Chapter 5 Wrap-Up 368 Summary 368 Enriching Your Mathematical Word Power 370 Review Exercises 371 Chapter 5 Test 374 Making Connections: A Review of Chapters Critical Thinking 376 Rational Expressions and Functions Properties of Rational Expressions and Functions 378 Multiplication and Division 388 Addition and Subtraction 396 Complex Fractions 407 Division of Polynomials 415 Solving Equations Involving Rational Expressions 425 Applications 433 Chapter 6 Wrap-Up 442 Summary 442 Enriching Your Mathematical Word Power 444 Review Exercises 445 Chapter 6 Test 449 Making Connections: A Review of Chapters Critical Thinking 452 Radicals and Rational Exponents ix Radicals 454 Rational Exponents 464 Adding, Subtracting, and Multiplying Radicals 475 Quotients, Powers, and Rationalizing Denominators 482 Solving Equations with Radicals and Exponents 491 Complex Numbers 502 Chapter 7 Wrap-Up 511 Summary 511 Enriching Your Mathematical Word Power 513 Review Exercises 514 Chapter 7 Test 518 Making Connections: A Review of Chapters Critical Thinking

4 dug33513_fm.qxd 11/20/07 3:22 PM Page x x Quadratic Equations, Functions, and Inequalities Factoring and Completing the Square 522 The Quadratic Formula 533 More on Quadratic Equations 543 Quadratic Functions and Their Graphs 552 Quadratic and Rational Inequalities 562 Chapter 8 Wrap-Up 576 Summary 576 Enriching Your Mathematical Word Power 577 Review Exercises 578 Chapter 8 Test 582 Making Connections: A Review of Chapters Critical Thinking 584 Additional Function Topics Graphs of Functions and Relations 586 Transformations of Graphs 598 Combining Functions 609 Inverse Functions 618 Variation 629 Chapter 9 Wrap-Up 637 Summary 637 Enriching Your Mathematical Word Power 639 Review Exercises 640 Chapter 9 Test 644 Making Connections: A Review of Chapters Critical Thinking 648 Exponential and Logarithmic Functions Exponential Functions and Their Applications 650 Logarithmic Functions and Their Applications 662 Properties of Logarithms 672 Solving Equations and Applications 680 Chapter 10 Wrap-Up 690 Summary 690 Enriching Your Mathematical Word Power 691 Review Exercises 691 Chapter 10 Test 695 Making Connections: A Review of Chapters Critical Thinking

5 dug33513_fm.qxd 11/20/07 3:22 PM Page xi Nonlinear Systems and the Conic Sections xi 699 Nonlinear Systems of Equations 700 The Parabola 709 The Circle 721 The Ellipse and Hyperbola 728 Second-Degree Inequalities 742 Chapter 11 Wrap-Up 748 Summary 748 Enriching Your Mathematical Word Power 751 Review Exercises 752 Chapter 11 Test 756 Making Connections: A Review of Chapters Critical Thinking 760 Sequences and Series (Available online at Sequences Series Arithmetic Sequences and Series Geometric Sequences and Series Binomial Expansions 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 Appendix A Geometry Review Exercises A-1 Answers to Selected Exercises Index A-1 A 3 I 1