# How can I implement a function that is a homomorphism?

I want to do the follow: Write a function $$f$$ such that if I evaluate $$f(ax+by)$$, it returns $$f(a)f(x)+f(b)f(y)$$. How can I do that? I tried to look in the help for "homomorphism" but didn’t find anything. I suspect there might be another name for this kind of functions in Mathematica.