Functions (expressions, relations, dependencies...) have shapes and they behave. Graphs show their (general, global. or local) shape or behavior. (When analyzed, they can turn out to be well-behaved or not (so) well-behaved.)
In math and physics, “wave” is understood to mean something dynamic, a magnitude dependent on location and time, and not necessarily periodic; “waves” are alive and move. A trigonometric function like y(x)=sin(x), being dependent on location only, is static, and the term “wave” doesn’t really apply to it.