Answer
Graph of the function as:
Work Step by Step
Substitute $x=-x$.
$\begin{align}
& f\left( x \right)=\frac{{{x}^{4}}}{{{x}^{2}}+2} \\
& f\left( -x \right)=\frac{{{\left( -x \right)}^{4}}}{{{\left( -x \right)}^{2}}+2} \\
& =\frac{{{x}^{4}}}{{{x}^{2}}+2} \\
& =f\left( x \right)
\end{align}$
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.
Since the degree of the numerator is less than the denominator, there is no horizontal asymptote.
For the vertical asymptote, equate the denominator to 0.
Thus, there are no real asymptotes.
