That is just lovely.
There are so many different variables used for the parameters in these combined transformations.
I’ve seen af(b(x-c))+d and af(b(x-h))+k most often.
K is also used as a constant of variation, but I haven’t seen it “inside” the function; when algebra 1 students encounter a K they often think of Y value of a vertex for x^2 or abs(x), or the Y translation. Would you consider changing the K to a different letter?
Yeah I debated about that for a while. I was going to go with just a,b,c,d as there’s no mathematical reason to favour k for anything in particular, including for shifts.
That said, there’s a long history of using k for compression and stretching via physics analog for springs constants and elasticity. Technically it should be an omega but assuming unit mass it’s a decent approximation for the physical aspect of stretching that gives real meaning to what that parameter physically represents.
That said, it’s entirely up to you! Just change the letter k to b in the note and nothing at all changes for the calculations. Zero dependencies means you can modify a lot and not worry it’s going to break or anything.