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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.
Fully integrated graphing calculator technology.
Workshop Precalculus: Discovery with Graphing Calculators
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