The question is, "Which of these relations on the set of all functions from $Z$ to $Z$ are equivalence relations.
I just want to make certain that I am interpreting this properly. So, (f,g) is an element in the relation, right? But it can only be an element if f and g, evaluated at one, are equal? And when the question says "of all functions," it means functions like f(x)=x^2? With this information, it can be reflexive, symmetric, and transitive, only if if f and g are the exact same functions, is that correct?