## Precalculus (6th Edition) Blitzer

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.