Let R = {(n, −n) | n ∈ Z and n ≤ 0} ∪ {(n, n + 1) | n ∈ N}. Is R a function? Justify your answer.

Answer 1

Yes. The two distinct pieces of the domain, the non-positive reals and the natural numbers, are mutually exclusive sets. Thus, having different function rules for each does not prevent R from being a function. If you wanted to have a visual representation to which you could apply the "vertical line test," the graph of R looks like the line y = -x for x ε (-∞ , 0] , and a line of points along y = x + 1 for n ∈ N.