Precalculus

Besides providing complete solutions to selected exercises in the text, this guide includes additional material for students who want a more intensive review of algebra and trigonometry. Also included in the guide are two copies of an examination - one copy to be taken at the beginning of the course to test their readiness for precalculus and a second copy to be used at the end of the course so students can assess their improvement and readiness for calculus.

CHAPTER 1 FUNCTIONS

1

(119)

1.1 Introduction

2

(1)

1.2 The Real Line

3

(10)

1.3 The Coordinate Plane

13

(8)

1.4 Equations and Graphs

21

(6)

1.5 Using Technology to Graph Equations

27

(9)

1.6 Functions

36

(16)

1.7 Linear Functions

52

(9)

1.8 Quadratic Functions

61

(13)

1.9 Other Common Functions

74

(8)

1.10 Arithmetic Combinations of Functions

82

(8)

1.11 Composition of Functions

90

(9)

1.12 Inverse Functions

99

(12)

Review Exercises

111

(6)

Exercises for Calculus

117

(3)

CHAPTER 2 ALGEBRAIC FUNCTIONS

120

(67)

2.1 Introduction

121

(1)

2.2 Polynomial Functions

122

(15)

2.3 Finding Factors and Zeros of Polynomials

137

(12)

2.4 Rational Functions

149

(17)

2.5 Other Algebraic Functions

166

(7)

2.6 Complex Roots of Polynomials

173

(7)

Review Exercises

180

(5)

Exercises for Calculus

185

(2)

CHAPTER 3 TRIGONOMETRIC FUNCTIONS

187

(89)

3.1 Introduction

188

(4)

3.2 The Sine and Cosine Functions

192

(11)

3.3 Graphs of the Sine and Cosine Functions

203

(12)

3.4 Other Trigonometric Functions

215

(8)

3.5 Trigonometric Identities

223

(11)

3.6 Right-Triangle Trigonometry

234

(10)

3.7 Inverse Trigonometric Functions

244

(11)

3.8 Applications of Trigonometric Functions

255

(15)

Review Exercises

270

(3)

Exercises for Calculus

273

(3)

CHAPTER 4 EXPONENTIAL AND LOGARITHM FUNCTIONS

276

(36)

4.1 Introduction

277

(2)

4.2 The Natural Exponential Function

279

(12)

4.3 Logarithm Functions

291

(10)

4.4 Exponential Growth and Decay

301

(7)

Review Exercises

308

(2)

Exercises for Calculus

310

(2)

CHAPTER 5 CONIC SECTIONS, POLAR COORDINATES, AND PARAMETRIC EQUATIONS

312

(55)

5.1 Introduction

314

(2)

5.2 Parabolas

316

(7)

5.3 Ellipses

323

(9)

5.4 Hyperbolas

332

(8)

5.5 Polar Coordinates

340

(11)

5.6 Conic Sections in Polar Coordinates

351

(6)

5.7 Parametric Equations

357

(5)

Review Exercises

362

(2)

Exercises for Calculus

364

(3)

ANSWERS TO SELECTED EXERCISES

367

(60)

INDEX

427

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