TEACHER NOTES

ISSUES RELATED TO THE PROBLEM

Prerequisites:

Prerequisites will vary depending on the functions used. I would envision using polynomials (up to cubic), sines, cosines, exponentials and logarithms.

It would probably be worth doing this exercise as a part of a general review of functions, and then again after the students have studied derivatives.

Time allotment - time management:

This will depend somewhat on the complexity of the functions being used, but 2-3 minutes for steps 1 and 2, 10-15 minutes for step 3, and 8-10 minutes for additional iterations seems about right.

Students who are stuck looking for a function should be instructed to sketch a graph that matches the description.

Expectations

Depending on the kinds of functions used, students could be asked to find the exact function or merely a generic version.

Future payoffs

The purpose of this exercise is to build the skills and intuition about functions that students need in order to, for example, choose an appropriate function form for a collection of data points.

Extensions

References and Sources