Workshop Precalculus: Discovery with Graphing Calculators, Preliminary Edition
June 2008, ©2002
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.
Preface. To The Student.
Activity P-1. Using the Concept of Function to Buy Pizza.
Activity P-2. Getting Started with Your Graphing Calculator.
UNIT 1. PROPERTIES OF FUNCTIONS.
Section 1. Analyzing Linear Functions.
Activity 1-1. Creating Linear Functions.
Activity 1-2. Investigating Piecewise-Linear Functions.
Activity 1-3. Interpreting Graphs.
Section 2. Analyzing Smooth Curves.
Activity 1-4. Developing an Intuitive Understanding of a Tangent Line to a Curve.
Activity 1-5. Investigating the Behavior of the Tangent Line Near a Turning Point.
Activity 1-7. Contemplating Concavity.
Activity 1-7. Interpreting Sign Charts.
Section 3. Representing Functions.
Activity 1-8. Evaluating Expressions and Using Variables.
Activity 1-9. Representing Functions Symbolically.
Activity 1-10. Representing Functions Graphically.
Activity 1-11. Representing Functions Numerically.
Activity 1-12. Constructing Discrete Functions.
UNIT 2. POLYNOMIAL AND RATIONAL FUNCTIONS.
Section 1. Power Functions.
Activity 2-1. Examining Positive Integer Power Functions.
Activity 2-2. Inspecting Negative Integer Power Functions.
Activity 2-3. Scrutinizing Root Functions.
Section 2. Polynomial Functions.
Activity 2-4. Probing Polynomials.
Activity 2-5. Finding the Vertex of a Parabola.
Activity 2-6. Drawing and Interpreting the Sign Chart for a Higher-Order Polynomial.
Activity 2-7. Examining the Multiplicity of a Zero of Polynomial.
Activity 2-8. Approximating the Turning Points and Investigating the Long-Run Behavior of a Polynomial.
Section 3. Rational Functions.
Activity 2-9. Locating Holes in Graphs of Rational Functions.
Activity 2-10. Investigating the Behavior of a Rational Function Near a Vertical Asymptote.
Activity 2-11. Locating the Intercepts of Rational Functions.
Activity 2-12. Analyzing the Long-Run Behavior of Rational Functions.
Activity 2-13. Sketching the Graph of a Rational Function.
UNIT 3. NEW FUNCTIONS FROM OLD.
Section 1. Combining Functions.
Activity 3-1. Evaluating Combinations of Functions.
Activity 3-2. Combining Functions.
Activity 3-3. Composing Functions.
Section 2. Reflecting Functions.
Activity 3-4. Sketching Reflections.
Activity 3-5. Representing Reflections Symbolically.
Activity 3-6. Investigating Inverse Functions.
Section 3. Shifting, Stretching, and Compressing Graphs of Functions.
Activity 3-7. Vertically Shifting a Graph.
Activity 3-8. Horizontally Shifting a Graph.
Activity 3-9. Vertically Stretching or Compressing a Graph.
Activity 3-10. Horizontally Stretching or Compressing a Graph.
Activity 3-11. Combing Transformations.
UNIT 4. MORE FUNCTION CLASSES.
Section 1. Exponential and Logarithmic Functions.
Activity 4-1. Modeling Situations Using Exponential Functions.
Activity 4-2. Comparing Exponential Functions.
Activity 4-3. Investigating the Relationship Between Exponential and Logarithmic Functions.
Activity 4-4. Evaluating and Graphing Logarithmic Functions.
Activity 4-5. Examining the Number e and the Natural Exponential and Logarithmic Functions.
Activity 4-5. Solving Exponential and Logarithmic Equations.
Section 2. Trigonometric Functions.
Activity 4-7. Measuring Angles.
Activity 4-8. Finding Trigonometric Functions of Acute Angles.
Activity 4-9. Evaluating Trigonometric Functions.
Activity 4-10. Graphing Trigonometric Functions.
Section 3. Analytic Trigonometry.
Activity 4-11. Defining Inverse Trigonometric Functions.
Activity 4-12. Solving Trigonometric Equations.
Activity 4-13. Verifying Multiple Angle Formulas.
Activity 4-14. Utilizing the Law of Cosines.
Activity 4-15. Utilizing the Law of Sines.
Section 4. Fitting Curves to Discrete Functions.
Activity 4-16. Modeling Data.
Appendix. Using the TI-83 Graphing Calculator in Workshop Precalculus.
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