Problem:
Given the family of functions

f(x) = a (x - b)3

with parameters a and b, determine what is the effect on the graph when you change the values of a and b.

Visualization:
Using Fortune (from the University of Arizona):

  1. After starting up the program, you are prompted "Would you like some instructions?" Use the arrow keys to move to either Yes or No and then press .
  2. If you choose Yes then read the instructions and press when you are ready to proceed.
  3. Use the arrow keys to highlight Function Operations and press .
  4. Use the arrow keys to highlight Create Function and press .
  5. At the prompt, f(x) =, type
    a*(x-b)^3 .
  6. Use the arrow keys to move to Plot Function and press .
  7. You will now see the graph of the function when a = 1 and b = 0. Each time that you type uppercase the value of a will be increased by one and the associated function plotted. By typing lowercase you will decrease a by one. Similarly, each time that you type uppercase the value of b will be increased by one and the associated function plotted. By typing lowercase you will decrease b by one.