Answer
The function is even.
Work Step by Step
$f(x)$ is even if $f(-x)=f(x).$ If so, it is symmetric relative to the y-axis.
$f(x)$ is odd if $f(-x)=-f(x).$ If so, it is symmetric relative to the origin.
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Replace x with $-x$ and check the result:
$f(-x)=(-x)^{4}-4(-x)^{2}=x^{4}-4x^{2}=f(x),$
meaning that the function is even.
Sketching the graph by taking some nonnegative values for x,
$\left[\begin{array}{ccccc}
x & 0 & 1 & 2 & 3\\
f(x) & 0 & -3 & 0 & 45
\end{array}\right]$ ,
we conclude that $(-1,-3), (-2,0),$ and $(-3,45)$ also belong to the graph