Must All Physically Reasonable Wavefunctions Remain Finite As $|x| \rightarrow \infty(A)$

Multiple Choice

Must all physically reasonable wavefunctions remain finite as $|x| \rightarrow \infty(A)$ , or does this apply only to solutions to the Schrödinger equation (B) ?

A) $|x| \rightarrow \infty$
B) Does this apply only to solutions to the Schrödinger equation