Answer
The graph of the function is:
Work Step by Step
Substitute $x=-x$ ,
$\begin{align}
& f\left( x \right)=\frac{2}{{{x}^{2}}+x-2} \\
& f\left( -x \right)=\frac{2}{{{\left( -x \right)}^{2}}+\left( -x \right)-2} \\
& =\frac{2}{{{x}^{2}}-x-2}
\end{align}$
Therefore, the function $f\left( -x \right)$ is not equal to $-f\left( x \right)$ and also $f\left( x \right)$. So, the graph of the function is neither symmetrical about the $y$-axis north the origin.
