Can I describe an arbitrary graph?

Question

This is, I think, a fairly simple question, but I haven't been able to find an answer to. Is there any graph for which there's no way to describe it in terms of a polynomial, function, or any other formula? If so, why?

Answer 1

I can draw (any) arbitrary curve that represents a function, but measuring what that function is exactly (with infinite precision) from the drawing is an insurmountable task.