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:

- Type in {1,2,3} STO A.
- Press ENTER.
- Type in {-1,0,1} STO B.
- Press ENTER.
- You can find the symbol "{" by pressing 2nd LIST and F1; the symbol "}" is then obtained by pressing F2.
- Press the GRAPH key and then pick y(x)= by pressing the F1 key.
- If necessary, keep pressing the F4 key until all preexisting graphs have been deleted.
- Be sure that PLOTS 1, 2, and 3 are turned off.
- At the prompt, \y1= , type in
A*(x-B)^3
- IMPORTANT
: "A" and "B" must be upper case, and, in order to avoid ERROR 13 DIMENSION, include the "*" sign.
- The WINDOW settings for the graph above are [-3, 3] × [-10, 10]:

- Select GRAPH by pressing F5.
- Note that the graphs of the functions are plotted in the order in which the values are stored in "A and B".
- 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.