Answer
Graph the function as:
Work Step by Step
Step 1: 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 $f\left( x \right)$. So, the graph of the function is neither symmetrical about the $y$-axis nor origin.
Step 2: To calculate the x intercept equate $f\left( x \right)=0$.
$-\frac{2}{{{x}^{2}}-x-2}=0$ ,
Which is not true for any value of x. Thus, there are no x-intercepts.
Step 3: To calculate the y intercepts evaluate $f\left( 0 \right)$.
$\begin{align}
& f\left( 0 \right)=-\frac{2}{{{0}^{2}}-0-2} \\
& f\left( 0 \right)=1 \\
\end{align}$
Step 4: Since the degree of the numerator is less than the denominator, there is no horizontal asymptote.
Step 5: For the vertical asymptote, equate the denominator to 0.
$\begin{align}
& {{x}^{2}}-x-2=0 \\
& x=-1,2
\end{align}$
