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Workshop Precalculus: Discovery with Graphing Calculators, Preliminary Edition

Workshop Precalculus: Discovery with Graphing Calculators, Preliminary Edition

Nancy Baxter Hastings

ISBN: 978-0-470-41251-0

Jun 2008

518 pages

Select type: Paperback

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Workshop Precalculus provides students with a bridge to the study of calculus and helps them develop the confidence, understanding, and skills necessary for continuing their study of mathematics.  Based on the premise that students learn better by doing and constructing their own knowledge, the Workshop approach involves instructors giving up some command and control of the classroom in favor of giving the students more responsibility for their own learning; this approach eliminates the distinction between classroom and laboratory work.

By systematizing and supporting a simple interactive teaching format, Workshop Precalculus helps instructors implement sound methods that alternate between three primary components: Summary Discussions, Introductory Remarks, and Collaborative Activities.  While students benefit greatly from performing computations and symbolic manipulations and sketching graphs by hand, the text integrates the use of the graphing calculator so that students learn to regard technology as a valuable tool.


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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

  • Fully integrated graphing calculator technology
  • The workshop approach:
    • Encourages students' guessing and estimation skills and promotes the development of intuitive skill
    • Stresses good reading and writing by asking students to explain what they observe
    • Allows students to discover the fun in math while learning new concepts and skills