Answer
odd
Work Step by Step
We know that if a function is odd, then $f(-x)=-f(x).$
We also 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*}
f(-x)&=\frac{-(-x)^3}{3(-x)^2-9}\\
&=\frac{x^3}{3x^2-9}\\
&=-\dfrac{-x^3}{3x^2-9}\\
&=-f(x)
\end{align*}
Therefore, the function is odd.
