How does the symmetry of $\displaystyle f(x) = \frac{p(x)}{q(x)}$ depend on the symmetry of $p(x)$ and $q(x)$? Select all true statements. There may be more than one correct answer.

A. If $p(x)$ and $q(x)$ are both even, then $f(x)$ is even.
B. If $p(x)$ is odd and $q(x)$ is even, then $f(x)$ is even.
C. If $p(x)$ is even and $q(x)$ is odd, then $f(x)$ is odd.
D. If $p(x)$ and $q(x)$ are both odd, then $f(x)$ is odd.
E. If $p(x)$ is even and $q(x)$ is odd, then $f(x)$ is even.
F. If $p(x)$ and $q(x)$ are both odd, then $f(x)$ is even.
G. If $p(x)$ or $q(x)$ is neither even nor odd, then $f(x)$ is neither even nor odd.
H. If $p(x)$ is odd and $q(x)$ is even, then $f(x)$ is odd.