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 the TI-86 graphing calculator:

1. Type in {1,2,3} STO A.
2. Press ENTER.
3. Type in {-1,0,1} STO B.
4. Press ENTER.
5. You can find the symbol "{" by pressing 2nd LIST and F1; the symbol "}" is then obtained by pressing F2.
6. Press the GRAPH key and then pick y(x)= by pressing the F1 key.
7. If necessary, keep pressing the F4 key until all preexisting graphs have been deleted.
8. Be sure that PLOTS 1, 2, and 3 are turned off.
9. At the prompt, \y1= , type in

A*(x-B)^3

10. IMPORTANT: "A" and "B" must be upper case, and, in order to avoid ERROR 13 DIMENSION, include the "*" sign.
11. The WINDOW settings for the graph above are [-3, 3] × [-10, 10]:

12. Select GRAPH by pressing F5.
13. Note that the graphs of the functions are plotted in the order in which the values are stored in "A and B".
14. Also note that only 3 lines were graphed although there are 9 combinations involving A and B. In order to make the TI-86 graph all 9 lines in the family, enter the parameters as follows:

{1,1,1,2,2,2,3,3,3} STO A

{-1,0,1,-1,0,1,-1,0,1}STO B

Constructed with the help of Chris O'Brien.