Answer
neither even nor odd
Work Step by Step
We know that if a function is odd, then $f(-x)=-f(x).$
We know that if a function is even, then $f(-x)=f(x).$
Hence, we plug in $-x$ into $x$ to see what happens.
\begin{align*}
h(-x)&=3(-x)^3+5\\
&=3\cdot(-x^3)+5\\
&=-3x^3+5
\end{align*}
This is neither $h(x)$ nor $h(-x)$, hence the function is neither even nor odd.
