Title Details

Nancy Baxter Hastings is the author of Workshop Precalculus: Discovery with Graphing Calculators, Preliminary Edition, published by Wiley.

Preface: to the Instructor ix

Preface: To the Student xv

Activity P-1: Using the Concept of Function to Buy Pizza xvi

Activity P-2: Getting Started with Your Graphing Calculator xviii

Unit 1: Properties of Functions 1

Section 1: Analyzing Linear Functions 1

Activity 1-1: Creating Linear Functions 3

Activity 1-2: Investigating Piecewise-Linear Functions 9

Activity 1-3: Interpreting Graphs 14

Section 2: Analyzing Smooth Curves 26

Activity 1-4: Developing an Intuitive Understanding of a Tangent Line to a Curve 27

Activity 1-5: Investigating the Behavior of the Tangent Line near a Turning Point 36

Activity 1-6: Contemplating Concavity 40

Activity 1-7: Interpreting Sign Charts 47

Section 3: Representing Functions 60

Activity 1-8: Evaluating Expressions and Using Variables 61

Activity 1-9: Representing Functions Symbolically 64

Activity 1-10: Representing Functions Graphically 72

Activity 1-11: Representing Functions Numerically 76

Activity 1-12: Constructing Discrete Functions 80

Unit 2: Polynomial and Rational Functions 97

Section 1: Power Functions 98

Activity 2-1: Examining Positive Integer Power Functions 99

Activity 2-2: Inspecting Negative Integer Power Functions 104

Activity 2-3: Scrutinizing Root Functions 110

Section 2: Polynomial Functions 127

Activity 2-4: Probing Polynomials 128

Activity 2-5 Finding the Vertex of a Parabola 138

Activity 2-6 Drawing and Interpreting the Sign Chart for a Higher-Order Polynomial 143

Activity 2-7: Examining the Multiplicity of a Zero of a Polynomial 148

Activity 2-8: Approximating the Turning Points and Investigating the Long-Run Behavior of a Polynomial 154

Section 3: Rational Functions 169

Activity 2-9: Locating Holes in Graphs of Rational Functions 170

Activity 2-10: Investigating the Behavior of a Rational Function near a Vertical Asymptote 174

Activity 2-11: Locating the Intercepts of Rational Functions 178

Activity 2-12: Analyzing the Long-Run Behavior of Rational Functions 182

Activity 2-13: Sketching the Graph of a rational Function 192

Unit 3: New Functions from Old 201

Section 1: Combining Functions 202

Activity 3-1: Evaluating Combinations of Functions 203

Activity 3-2: Combining Functions 208

Activity 3-3: Composing Functions 217

Section 2: Reflecting Functions 226

Activity 3-4: Sketching Reflections 227

Activity 3-5: Representing Reflections Symbolically 232

Activity 3-6: Investigating Inverse Functions 242

Section 3: Shifting, Stretching, and Compressing Graphs of Functions 259

Activity 3-7: Vertically Shifting a Graph 261

Activity 3-8: Horizontally Shifting a Graph 266

Activity 3-9: Vertically Stretching or Compressing a Graph 274

Activity 3-10: Horizontally Stretching or Compressing a Graph 280

Activity 3-11: Combining Transformations 288

Unit 4: More Function Classes 301

Section 1: Exponential and Logarithmic Exponential Functions 302

Activity 4-1: Modeling Situations Using Exponential Functions 303

Activity 4-2: Comparing Exponential Functions 309

Activity 4-3: Investigating the Relationship between Exponential and Logarithmic Functions 318

Activity 4-4: Evaluating and Graphing Logarithmic Functions 323

Activity 4-5: Examining the Number e and the Natural Exponential and Logarithmic Functions 329

Activity 4-6 Solving Exponential and Logarithmic Equations 334

Section 2: Trigonometric Functions 348

Activity 4-7: Measuring Angles 352

Activity 4-8: Finding Trigonometric Functions of Acute Angles 358

Activity 4-9: Evaluating Trigonometric Functions 366

Activity 4-10: Graphing Trigonometric Functions 380

Section 3: Analytic Trigonometry 405

Activity 4-11: Defining Inverse Trigonometric Functions 406

Activity 4-12: Solving Trigonometric Equations 416

Activity 4-13: Verifying Multiple Angle Formulas 428

Activity 4-14: Utilizing the Law of Cosines 433

Activity 4-15: Utilizing the Law of Sines 439

Section 4: Fitting Curves to Discrete Functions 455

Activity 4-16: Modeling Data 456

Appendix: Using the TI-83 Graphing Calculator in Workshop Precalculus 465

Index 509