I want to express the simple idea that two functions f and g are related in the following way:
$$ f(x) > f(y) \implies g(x) > g(y) $$
Or the inverse relation:
$$ f(x) > f(y) \implies g(x) < g(y) $$
I was going to use the term "proportional" or "inversely proportional", but I understand that in mathematics that implies a linear (or inverse linear) relationship, which is not my case. Is there a better term to express this than something like "$f(x)$ increases as $g(x)$ increases/decreases"?