Which of the Following Statements Are True? Select All That $f(x)$

Multiple Choice

Which of the following statements are true? Select all that apply.

A) If $f(x)$ is an even function, then its graph is symmetric about the $y$ -axis.
B) $g(x) =x^{5}+\cos (7 x)$ is an odd function.
C) $h(x) =x^{5} \cdot \cos (7 x)$ is an odd function.
D) If $f(x)$ is an even function, then $\int_{-4}^{4} f(x) d x=0$ .
E) If $j(x)$ is an odd function with the Fourier series representation
$f(x) \sim \frac{a_{0}}{2}+\sum_{n=1}^{\infty} a_{n} \cos \frac{n \pi t}{5}+b_{n} \sin \frac{m \pi t}{5}$ , then $a_{n}=0$ , for all $n$ .