Answer
The function f is an even function and symmetric about the $y-\text{axis}$.
Work Step by Step
Substitute $x$ with $-x$ in the given function and simplify as below:
$\begin{align}
& f\left( -x \right)={{\left( -x \right)}^{2}}\sqrt{1-{{\left( -x \right)}^{2}}} \\
& f\left( -x \right)={{x}^{2}}\sqrt{1-{{x}^{2}}} \\
& f\left( -x \right)=f\left( x \right)
\end{align}$
On putting –x in the place of x, it can be seen that same function is obtained. Thus the definition of an 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 $y-\text{axis}$.
