How do you determine if a set of ordered pairs is a function or not?

You could set up the relation as a table of ordered pairs. Then, test to see if each element in the domain is matched with exactly one element in the range. If so, you have a function! Watch this tutorial to see how you can determine if a relation is a function.

A function is a set of ordered pairs in which no 2 pairs with the same first element have a different second element. 

If you think about it, it makes sense. Think about  f(x) = x + 1. The pairs (x, f(x)) look like (1,2), (2,3), (3,4), (4,5), etc. If you also had (1,3) in the set, then there'd be two different answers for 1+1. The same applies to any function. There can only be one result for a given input value. Your welcome!!