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It depends on whether fx denotes frequency times variable value or the probability generating function for the variable x.
If it were written in a book of some sort, fx or f(x) is read aloud as "f or x". "f" is a function of some variable, "x". By function it means something happens to x e.g. x2 or 3x+4.
Even (unless c = 0 in which case it is either or both!)
Yes. It is a piece-wise function with the limit: lim{x->0}= 0 You graph both parts as two series of dotted lines since there are infinite rational and irrational possibilities