Mathematics 136, Section 3 – AP Calculus, Section 4 Discussion 1–Matching Formulas to Graphs September 9, 2003

Background

We have been reviewing the basic functions studied in calculus. Today, in a group discussion exercise, we will conclude this initial part of the course. Given a graph, we will try to determine a reasonable formula that might yield a graph with that shape. An additional goal will be to introduce you to a way of working in a classroom context you may not have experienced too often before in mathematics classes – collaborative learning. Some suggestions:

• Try to tackle the questions below as a group, not individually. For instance, don’t be shy about throwing out partial ideas or suggestions how to proceed. That’s the point of doing things this way, and you’re “in this” together.

• The goal is for everyone to contribute to, and fully understand the group’s results. So if you think you “see” something, your job is to explain it to the other members of the group. On the other hand, if you don’t understand something someone else says, your job is to ask questions until either you are convinced, or you are able to show the other person that he or she was mistaken.

• Choose one or more “scribe(s)” within your group to keep a clean written record of what you do. The end product of the exercise will be one set of solutions to the problems below, which you will turn in as a group. I will assign one grade for each group’s solutions.

Discussion Questions

Find a possible formula for each of the functions defined by the graphs in problems 6-17 in the Review Problems for Chapter 1 on page 49 of our text. Important Directions: No calculators, graphing or otherwise, may be used during the class discussion(!)

Some suggestions

• Start by trying to determine what family of functions fits the properties of each graph the best (i.e. is it the graph of a linear function, an exponential function, a polynomial function, a trigonometric function, a rational function?)

• Once you have decided what type of function you are dealing with, you may also need to determine constants, and shift and/or scale the basic functions we have studied to get a graph like the one shown.

• NOTE: There are many different correct answers for each of these, but some correct answers are also very complicated. There are relatively “simple” formulas that will work in each case!

Due: In class, Wednesday, September 10.