**Problem Books**

Volume: 29;
2018;
218 pp;
Softcover

MSC: Primary 97;

**Print ISBN: 978-1-4704-4349-8
Product Code: PRB/29**

List Price: $30.00

AMS Member Price: $22.50

MAA Member Price: $22.50

**Electronic ISBN: 978-1-4704-4886-8
Product Code: PRB/29.E**

List Price: $30.00

AMS Member Price: $22.50

MAA Member Price: $22.50

# Functions and Graphs: A Clever Study Guide

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*James Tanton*

MAA Press: An Imprint of the American Mathematical Society

A playful, readable, and thorough guide to precalculus, this book
is directed at readers who would like a holistic look at the high
school curriculum material on functions and their graphs. Tanton
provides a coherent guided tour of exploration and discovery of a rich
mathematical landscape. The exploration is presented through problems
selected from the history of the Mathematical Association of America's
American Mathematics Competition (AMC).

Secondary school teachers looking for supplementary and enrichment
materials will find this a rich resource, which aligns with national
curriculum standards. High school and college calculus and
precalculus students will discover an approachable and
thought-provoking review, preview, and overview of these central
mathematical ideas. Students preparing for the AMC should find it
especially helpful. Active reading, with pencil in hand, will result
in a deep appreciation and understanding of the properties of
functions.

James Tanton is the MAA's mathematician-at-large. A research
mathematician with experience teaching at both the college and high
school levels, he now works to encourage and aid all mathematics
instructors to teach—and all mathematics students to
learn—joyously and effectively.

#### Readership

Undergraduate students interested in teaching secondary mathematicis, high school-level contest problems, and math circles for teachers.

#### Reviews & Endorsements

The success here is two-fold, one of tone and explanation while also tackling topics not typically seen at this level, yet key to later success.

-- Tom Schulte, MAA Reviews

#### Table of Contents

# Table of Contents

## Functions and Graphs: A Clever Study Guide

- Cover Cover11
- Functions and Graphs ii3
- Copyright iv5
- Contents v6
- About These Study Guides ix10
- This Guide and Mathematics Competitions xi12
- This Guide and the Craft of Solving Problems xv16
- This Guide and Mathematics Content: Functions and Graphs xvii18
- Part I . Functions and Graphs 120
- Chapter 1. What Is a Function? A Swift Conceptual Overview 322
- Chapter 2. Sequences as Functions on ℕ 2140
- Chapter 3. Numerical Functions on ℝ 3958
- Chapter 4. Composite Functions and Inverse Functions 4564
- Chapter 5. Graphing 5372
- Chapter 6. Transformations of Graphs 7190
- Chapter 7. Average Rate of Change, Constant Rate of Change 89108
- Chapter 8. Quadratic Functions 101120
- Chapter 9. Polynomial Functions 129148
- Chapter 10. Rational Functions 151170
- Chapter 11. Select Special Functions and Equations 167186
- Chapter 12. Fitting Formulas to Data Points 179198

- Part II . Solutions 189208
- Part III . Appendices 209228
- Appendix I. Ten Problem-Solving Strategies 211230
- 1. Engage in Successful Flailing 211230
- 2. Do Something! 211230
- 3. Engage in Wishful Thinking 212231
- 4. Draw a Picture 212231
- 5. Solve a Smaller Version of the Same Problem 212231
- 6. Eliminate Incorrect Choices 213232
- 7. Perseverance Is Key 213232
- 8. Second-Guess the Author 213232
- 9. Avoid Hard Work 214233
- 10. Go to Extremes 214233

- Appendix II. Connections to the Common Core State Standards: Practice Standards and Content Standards 215234

- Back Cover Back Cover1238