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Workshop Precalculus: Discovery with Graphing Calculators, Preliminary Edition

June 2008, ©2002
Workshop Precalculus: Discovery with Graphing Calculators, Preliminary Edition (EHEP000287) cover image
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.

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.

Index.

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  • 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
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Instructors Resources
Wiley Instructor Companion Site
Workshop Precalculus: Discovery with Graphing Calculators Preliminary Edition Istructor Resources
The Instructor Resources to accompany Workshop Precalculus help instructors create a fully investigative and collaborative learning environment for students and support a simple "interactive teaching format" which consists of: Introductory Remarks, Collaborative Activities, and Summary Discussions. With the help of the Instructor Resources, all motivated faculty members can make the transition, with minimal obstacles, from the course they've always taught to the course they've always wanted to teach.
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Purchase Options
Paperback   
Workshop Precalculus: Discovery with Graphing Calculators, Preliminary Edition
ISBN : 978-0-470-41251-0
518 pages
June 2008, ©2002
$118.95   BUY

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