Naming functions that students can use

I would like to be able to name a function, potentially in a graph component, and then allow students to use that name in a math input.
For example, on slides 1, 2, and 4, I wish my students could write the integral of f(y)-g(y) or similar.

Is this possible?

It would work in a full screen graph, but can’t really do it in math inputs without doing something a little hacky (i.e. treating f and g as variables).