Question

Does the graph of any relation have end behaviors that can be described the same way as the end behaviors of a polynomial relation?

Answer 1

No

Explanation:

Not all relations have either an infinite domain or an infinite range. Some have no "end behavior". A sine function, for example, continues to oscillate between -1 and +1 forever.

The graphs of some relations are simply a collection of points, so the "end behavior" would be the points at either extreme of the domain.