Question

is {(1,3),(2,3),(3,4)} a function?

Answer 1

i think the answer is no but not sure if you can't have 2 of the same range or is it two of the same domains?

Answer 2

I would call it a set, of three ordered pairs.
As such, one could wonder if these ordered pairs could be the x and f(x) of a function.
I don't see why not. After all, what defines a function f, is the rule that for each x in the domain, there is one number that is its "image", or f(x).
If we have the domain {1, 2, 3}, then the corresponding images are {3, 4}, so indeed there is an f(x) for each x: f(1) = 3, f(2) = 3 and f(3) = 4.
The ordered pairs could be considered as the graph of f.

Answer 3

It is a function because a function cannot have two of same domain.