This last activity is intended to help you understand the different kinds of dilations (aka stretches) that are possible when you multiply a function by a constant.
There are two sliders: a is intended primarily for values >1, and b is intended for fractions/decimals between -1 and 1.
f(x) is the parent function. I started you out with f(x) = sin(x) because it shows the different dilations well, but after you play around with it some, you can change it to a different parent function.
The other functions are defined as follows and should not be changed:
g(x) = f(x) * a
h(x) = f(x) * b
k(x) = f(a*x)
m(x) = f(b*x)
Notice how the function rules themselves change as you adjust the sliders, and also notice what happens to the graph. When you think you understand what these four different transformations do, write down your ideas.