A library of functions: Functions and their graphs

These activities were taken from the review chapter in the Calculus book that is the successor of this course's Precalculus book. In addition to the kinds of functions explored in Chapter 9: Polynomial and Rational Functions, a review of functions explored earlier in the course (e.g., sinusoidal functions) are also explored.

Power, polynomial and rational functions

This week's handout reviews the fundamental aspects of these three types of function, and polynomial and rational functions are seen as combinations of other functions.

Compositions, Inverses, and Translations of Functions

If the course had proceeded from a function-based approach, the concepts in Chapter 8 would have appeared in Chapter 1. That would have been helpful to students so that they could see patterns across the ways we act on functions. Although that's not the case, students have seen some of the techniques covered in this chapter in the earlier chapters. Perhaps this is an attempt to "draw things together."

Download the problem set here.

Applying a few of the trig identities

These 3 problems are interesting demonstrations of the usefulness of trig identities. Even better, the paths to the solutions are interesting and the solutions themselves are surprising.

Have fun.