Families of functions

Graphapplet has provisions to plot several members of a family of functions
Example 1
Suppose we want to investigate fp(x)=x3-3px for p=-2,-1,0,1 and 2
We enter:
<PARAM name=function1 value="x^3-3*p*x;p=-2,-1,0,1,2">

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Example 2
Suppose we enter
<PARAM name=function1 value="a*x+b;a=-2,-1,1,2;b=-2,0,2">

GraphApplet calculates all possible combinations of a and b (4*3=12) and plots the aasociated line.
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Example 3
As you see plotting families of functions may take quite a time. If you use the user function some families can be plotted faster. Enter:

<PARAM name=function1 value="user:line;a=-2,-1,1,2;b=-2,0,2">

The values of a and b are now presented to a precompiled user function, so string evaluation need not be done every time again
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A full discussion of the user option can be found at Faster Plotting.