Answer
Graph the function as:
Work Step by Step
Substitute $x=-x$.
$\begin{align}
& f\left( x \right)=\frac{2{{x}^{4}}}{{{x}^{2}}+1} \\
& f\left( -x \right)=\frac{2{{\left( -x \right)}^{4}}}{{{\left( -x \right)}^{2}}+1} \\
& =\frac{2{{x}^{4}}}{{{x}^{2}}+2} \\
& =f\left( x \right)
\end{align}$
Therefore, the function $f\left( -x \right)$ is equal to $-f\left( x \right)$. The graph of the function is symmetric about the $y$ -axis and origin.
