About the Author v

Preface to the Instructor xv

WileyPLUS xxi

Acknowledgments xxii

Preface to the Student xxiv

**0 The Real Numbers 1**

0.1 The Real Line 2

0.2 Algebra of the Real Numbers 7

0.3 Inequalities, Intervals, and Absolute Value 23

Chapter Summary and Chapter Review Questions 40

**1 Functions and Their Graphs 41**

1.1 Functions 42

1.2 The Coordinate Plane and Graphs 55

1.3 Function Transformations and Graphs 69

1.4 Composition of Functions 90

1.5 Inverse Functions 104

1.6 A Graphical Approach to Inverse Functions 119

Chapter Summary and Chapter Review Questions 129

**2 Linear, Quadratic, Polynomial, and Rational Functions 133**

2.1 Lines and Linear Functions 134

2.2 Quadratic Functions and Conics 150

2.3 Exponents 174

2.4 Polynomials 193

2.5 Rational Functions 208

Chapter Summary and Chapter Review Questions 223

**3 Exponential Functions, Logarithms, and e 225**

3.1 Logarithms as Inverses of Exponential Functions 226

3.2 Applications of the Power Rule for Logarithms 237

3.3 Applications of the Product and Quotient Rules for Logarithms 247

3.4 Exponential Growth 260

3.5 *e* and the Natural Logarithm 278

3.6 Approximations and area with e and ln 292

3.7 Exponential Growth Revisited 302

Chapter Summary and Chapter Review Questions 311

**4 Trigonometric Functions 313**

4.1 The Unit Circle 314

4.2 Radians 329

4.3 Cosine and Sine 343

4.4 More Trigonometric Functions 355

4.5 Trigonometry in Right Triangles 367

4.6 Trigonometric Identities 377

Chapter Summary and Chapter Review Questions 390

**5 Trigonometric Algebra and Geometry 393**

5.1 Inverse Trigonometric Functions 394

5.2 Inverse Trigonometric Identities 408

5.3 Using Trigonometry to Compute Area 417

5.4 The Law of Sines and the Law of Cosines 431

5.5 Double-Angle and Half-Angle Formulas 448

5.6 Addition and Subtraction Formulas 462

Chapter Summary and Chapter Review Questions 472

**6 Applications of Trigonometry 475**

6.1 Transformations of Trigonometric Functions 476

6.2 Polar Coordinates 493

6.3 Vectors 504

6.4 Complex Numbers 518

6.5 The Complex Plane 531

Chapter Summary and Chapter Review Questions 540

**7 Sequences, Series, and Limits 541**

7.1 Sequences 542

7.2 Series 557

7.3 Limits 576

Chapter Summary and Chapter Review Questions 589

**8 Systems of Linear Equations 591**

8.1 Solving Systems of Linear Equations 592

8.2 Matrices 604

Chapter Summary and Chapter Review Questions 616

**Appendix A: Area 617**

Circumference 617

Squares, Rectangles, and Parallelograms 618

Triangles and Trapezoids 620

Stretching 621

Circles and Ellipses 622

Exercises and Problems 625

**Appendix B: Parametric Curves 629**

Curves in the Coordinate Plane 629

Graphing Inverse Functions as Parametric Curves 634

Shifting, Stretching, or Flipping a Parametric Curve 635

Exercises and Problems 638

Photo Credits 640

Index 641