A is the set of all functions $\mathbb{R}$ $\to$ $\mathbb{R}$
f is related to g if and only if f(x) $\le$ g(x) for all x $\in$ $\mathbb{R}$
I said its reflexive since it is less than OR equal, so f(x)=f(x)
However would it be symmetric and transitive?
I said it would not be symmetric (counter-example) because take x,y $\in$ $\mathbb{R}$ if x=3, y=10 then it would not be symmetric but i'm not too sure...
Also since it is a partial order, is it a total order?
It is surely not symmetric, as you pointed out in your question. It is actually anti-symmetric, hence your relation (being also reflexive and transitive) turns out to be a (partial) order, not an equivalence.