A relation is a function if and only if given two pairs (a,b) and (c,d), if a=c then b=d. This means that for a single value a, there cannot be two different values associated to it.
Since the pairs (16,-2) and (16,2) are in the relation but 2 is different from -2, then this relation is NOT a function.
Another counterexample is the number 1, since the pairs (1,-1) and (1,1) belong to the relation but the second entries -1 and 1 are different.