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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.
Functions and Graphs
What Is a Function? A Swift Conceptual Overview
Sequences as Functions on ℕ
Numerical Functions on ℝ
Composite Functions and Inverse Functions
Graphing
Transformations of Graphs
Average Rate of Change, Constant Rate of Change
Quadratic Functions
Polynomial Functions
Rational Functions
Select Special Functions and Equations
Fitting Formulas to Data Points
Solutions
Appendices
Appendix I. Ten Problem-Solving Strategies
Appendix II. Connections to the Common Core State Standards: Practice Standards and Content Standards