Using f(x) isn’t as straightforward as one would like. I put together a similar transformation activity, but I borrowed from Mike Gleeson on this CL Forum for the nuts and bolts of animating the transformation using af\left(B\left(x-h\right)\right)+k
Function Transformation Component
I added a screen to your activity that should work for what you are wanting students to enter.
Note, when I first started trying to code in CL I found an activity I liked and tried to make sense of it.