For FULL activity visit
Students find transforming functions one of the most demanding topics in mathematics at this level. In particular, the effect a has on the function, f(x) for y=af(x) and y=f(ax) and understanding just what a stretch is. This activity documents the most succesful approach I've had with this topic. It approaches the idea from the angle of transforming shapes, looking at the effect on the coordinates, then applying the same transformations to graphs.
This is a very complete activity that makes use of Geogebra and includes ready made applets and help videos for teachers who may have little experience or confidence in using technology in the classroom. Watch the following video (no sound) to get an overview of the activity: