People often find graph transformations tricky. I know I did when I was at school. So I've written a couple of documents to try and help. One of the problems is that when you do transformations, you should be thinking not only of transforming the graph, but of transforming the equation as well. The two go together. That's why I've called the process 'Function Transformations', rather than the more common 'Graph Transformations'!
The first is aimed at AS-level students, to show you the basics of shift and scaling (compressions and stretches):
And the second covers reflections and the modulus operation:
A couple of documents covering shift, scaling, reflection and modulus transformations.
If you would like to get in touch, e-mail me!