Transformations Across functions

So our lesson in class was about transforming any function, f(x) using generalization (stating: y=f(x), y= -3f(1/2(x-2))+3 etc.)

The homework question is the one thing that may have been the most basic, but I think that because it was so easy, we dismissed discussing it: How do you take points that were in f(x) and find their corresponding points in the transformed function?

Example:

You have the points (2,3), (4,6), (8,9) on y=f(x). Find their corresponding point on y= -2f(2x)+3 .

My first guess would simply be to plug x and y in to the transformed function but I don't want to assume in this case. I'd just like to double check. Confirmation?