Functions Modeling Change: A Preparation for Calculus

An accessible Precalculus text with concepts, examples, and problems

The sixth edition of Functions Modeling Change: A Preparation for Calculus helps students establish a foundation for studying Calculus. The text covers key Precalculus topics, examples, and problems. Chapters examine linear, quadratic, logarithmic, exponential, polynomial, and rational functions. They also explore trigonometry and trigonometric Identities, plus vectors and matrices. The end of each chapter offers details on how students can strengthen their knowledge about the topics covered.

1 Linear Functions and Change 1

1.1 Functions and Function Notation 2

1.2 Rate of Change 10

1.3 Linear Functions 19

1.4 Formulas For Linear Functions 28

1.5 Graphs and Models With Linear Functions and Inequalities 40

1.6 Fitting Linear Functions To Data 49

Strengthen Your Understanding 55

2 Functions 57

2.1 Input and Output 58

2.2 Domain and Range 67

2.3 Piecewise-Defined Functions 73

2.4 Preview of Transformations: Shifts 81

2.5 Preview of Composite and Inverse Functions 88

2.6 Concavity 97

Strengthen Your Understanding 103

3 Quadratic Functions 105

3.1 Introduction To The Family Of Quadratic Functions 106

3.2 The Vertex of a Parabola 113

Strengthen Your Understanding 120

4 Exponential Functions 121

4.1 Introduction To The Family Of Exponential Functions 122

4.2 Comparing Exponential and Linear Functions 131

4.3 Graphs of Exponential Functions 140

4.4 Applications To Compound Interest 149

4.5 The Number E 152

Strengthen Your Understanding 161

5 Logarithmic Functions 163

5.1 Logarithms and Their Properties 164

5.2 Logarithms and Exponential Models 173

5.3 The Logarithmic Function and Its Applications 181

5.4 Logarithmic Scales 192

Strengthen Your Understanding 203

6 Transformations of Functions and Their Graphs 205

6.1 Shifts, Reflections, and Symmetry 206

6.2 Vertical Stretches and Compressions 215

6.3 Horizontal Stretches and Combinations Of Transformations 223

Strengthen Your Understanding 233

7 Trigonometry Starting with Circles 235

7.1 Introduction To Periodic Functions 236

7.2 The Sine and Cosine Functions 241

7.3 Radians and Arc Length 248

7.4 Graphs of Sine and Cosine Functions 255

7.5 Sinusoidal Functions 263

7.6 The Tangent Function 272

7.7 The Six Trigonometric Functions and Relationships Between Them 276

7.8 Inverse Trigonometric Functions 282

Strengthen Your Understanding 287

8 Trigonometry Starting with Triangles 291

8.1 Trig Functions and Right Triangles 292

8.2 Non-Right Triangles 302

Strengthen Your Understanding 311

9 Trigonometric Identities, Polar Coordinates, and Complex Numbers 313

9.1 Trigonometric Equations 314

9.2 Identities, Expressions, and Equations 319

9.3 Sum and Difference Formulas For Sine and Cosine 327

9.4 Polar Coordinates 332

9.5 Complex Numbers and De Moivre’s Theorem 339

Strengthen Your Understanding 347

10 Compositions, Inverses, and Combinations of Functions 349

10.1 Revisiting Composition of Functions 350

10.2 Revisiting Inverse Functions 358

10.3 The Graph, Domain, and Range of An Inverse Function 365

10.4 Combinations of Functions 370

Strengthen Your Understanding 381

11 Polynomial and Rational Functions 383

11.1 Power Functions and Proportionality 384

11.2 Polynomial Functions and Their Behavior 395

11.3 Zeros of Polynomials and Short-Run Behavior 404

11.4 Rational Functions 410

11.5 The Short-Run Behavior of Rational Functions 417

11.6 Comparing Power, Exponential, and Log Functions 425

11.7 Fitting Exponentials and Polynomials To Data 432

Strengthen Your Understanding 439

12 Vectors and Matrices 441

12.1 Vectors 442

12.2 The Components Of A Vector 450

12.3 Applications Of Vectors 458

12.4 The Dot Product 465

12.5 Matrices 471

Strengthen Your Understanding 483

Answers to Odd-Numbered Problems 484

Index 515