Precalculus (10th Edition)

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.