#### Answer

The function is an even function and the graph of the function is symmetric about the $y-\text{axis}$.

#### Work Step by Step

An odd function is the function having symmetry with the origin and an even function is the function having symmetry with the y-axis.
To check whether the function is even or odd, substitute $-x$ in the place of $x$ in the function and simplify as follows:
$\begin{align}
& f\left( -x \right)=\frac{1}{5}{{\left( -x \right)}^{6}}-3{{\left( -x \right)}^{2}} \\
& f\left( -x \right)=\frac{1}{5}{{x}^{6}}-3{{x}^{2}} \\
& f\left( -x \right)=f\left( x \right)
\end{align}$
On putting –x in the place of x, it can be seen that the same function is obtained. Thus the definition of even function is fulfilled. And, the graph of the function is symmetric about the $y-\text{axis}$.
Hence, the function is an even function and the graph of the function is symmetric about the $y-\text{axis}$.