Wilson's Precalculus Guide
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The Rule of Four— A Balanced Approach A principal feature of this edition is the balance among the algebraic, numerical, graphical, and verbal methods of representing problems: the rule of four. For instance, we obtain solu-tions algebraically when that is the most appropriate technique to use, and we obtain solutions graphically or numerically when algebra is difficult to use. We urge students to solve prob-lems by one method and then support or confirm their solutions by using another method. We believe that students must learn the value of each of these methods or representations and must learn to choose the one most appropriate for solving the particular problem under considera-tion. This approach reinforces the idea that to understand a problem fully, students need to understand it algebraically as well as graphically and numerically.
Problem- Solving Approach Systematic problem solving is emphasized in the examples throughout the text, using the following variation of Polya’s problem- solving process:
• understand the problem,
• develop a mathematical model,
• solve the mathematical model and support or confirm the solutions, and
• interpret the solution. Students are encouraged to use this process throughout the text.
Twelve Basic Functions Twelve basic functions are emphasized throughout the book as a major theme and focus. These functions are:
• The Identity Function • The Squaring Function • The Cubing Function • The Reciprocal Function • The Square Root Function • The Exponential Function • The Natural Logarithm Function • The Sine Function • The Cosine Function • The Absolute Value Function • The Greatest Integer Function • The Logistic Function