I believe an "f" curve depicts the position of something as a function of time. "f" is simply because the position curve looks like an "f". I've also heard it called an "s" curve. It is generated by using a constant positive acceleration followed by a constant negative acceleration. The opposing accelerations result in zero velocity at the target position. If you integrate the accelerations you get velocity, then if you integrate the velocity you get position. BTW, thank you for your excellent presentations.
A while back I Asked around to the other devs the origin of F curve is lost to history. Function curve, frame curve, something else? No one was 100% sure.
If you landed here first, stay strong and graph edit your face off, otherwise you will die a slow agonizing death trying to get timeline, dope sheet, or NLA to bend to your will and ultimately will find yourself back here at the graph editor, with a bigger monitor and dedicated view tab;). I have yet to find anything in the other options that can’t be done quicker, more accurately or really more fun in GE 😂 good luck.