This aplet lets you dilate a parent function horizontally or vertically.
There are two functions shown: a parent function in black and a dilation of it in green. At first, you can only see the dilation because it is in front of the parent.
The dilation is either vertical (change the value of "a") or horizontal (change the value of "b") or both. Experiment and observe where the labeled points are moved to.
Notice that the equation for the dilation is (y/a) = f(x/b), which is equivalent to y = a*f((1/b)*x), which is the format many books use but seems pretty darn awkward and hard to wrap your head around. Stick with (y/a) = f(x/b) and you'll go far.