## Precalculus (6th Edition) Blitzer

The function is an even function and the graph of the function is symmetric about the $y-\text{axis}$.
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 given function is even or odd, substitute x with $-x$ in the provided function and simplify as follows: \begin{align} & f\left( -x \right)=2{{\left( -x \right)}^{2}}+{{\left( -x \right)}^{4}}+1 \\ & f\left( -x \right)=2{{x}^{2}}+{{x}^{4}}+1 \\ & 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. The graph of the function is symmetric about the $y-\text{axis}$ and thus the definition of even function is fulfilled. Hence, the function is an even function and the graph of the function is symmetric about the $y-\text{axis}$.