Precalculus

1. Warming Up
2. Imposing Coordinates
3. Three Simple Curves
4. Linear Modeling
5. Functions and Graphs
6. Graphical Analysis
7. Quadratic Modeling
8. Composition
9. Inverse Functions
10. Exponential Functions
11. Exponential Modeling
12. Logarithmic Functions
13. Three Construction Tools
14. Rational Functions
15. Measuring an Angle
16. Measuring Circular Motion
17. The Circular Functions
18. Trigonometric Functions
19. Sinusoidal Functions
20. Inverse Circular Functions

Prior to 1990, the performance of a student in precalculus at the University of Washington was not a predictor of success in calculus. For this reason, the mathematics department set out to create a new course with a specific set of goals in mind:

• A review of the essential mathematics needed to succeed in calculus.
• An emphasis on problem solving, the idea being to gain both experience and confidence in working with a particular set of mathematical tools.

This text was created to achieve these goals and the 2004-05 academic year marks the eleventh year in which it has been used. Several thousand students have successfully passed through the course.

This book is full of worked out examples. We use the the notation “Soluion.” to indicate where the reasoning for a problem begins; the symbol ?? is used to indicate the end of the solution to a problem. There is a Table of Contents that is useful in helping you find a topic treated earlier in the course. It is also a good rough outline when it comes time to study for the final examination. The book also includes an index at the end. Finally, there is an appendix at the end of the text with ”answers” to most of the problems in the text. It should be emphasized these are ”answers” as opposed to ”solutions”. Any homework problems you may be asked to turn in will require you include all your work; in other words, a detailed solution. Simply writing down the answer from the back of the text would never be sufficient; the answers are intended to be a guide to help insure you are on the right track.