Transformation Sliders

Author:
SFK
You may change f(x) to different functions. t(x) is a transformation of f(x) such that t(x) = a(f( (x-r)/c ) + d You may move the sliders to try different values for a, b, c, d.
What does a do? What does b do? What does c do? What does d do? Are there ranges where the behavior changes? try a>1, 0<a<1, a<0 And describe each separately. Find ranges of behavior for the other functions.