Answer
Graph of the function is:
Work Step by Step
Step 1: Substitute $x=-x$
$\begin{align}
& f\left( x \right)=\frac{x+2}{{{x}^{2}}+x-6} \\
& f\left( -x \right)=\frac{\left( -x \right)+2}{{{\left( -x \right)}^{2}}+\left( -x \right)-6} \\
& =\frac{-x+2}{{{x}^{2}}-x-6}
\end{align}$
Therefore, the function $f\left( -x \right)$ is not equal to either $-f\left( x \right)$ or $f\left( x \right)$. Hence, the graph of the function is symmetrical neither about the $y$ -axis nor about the origin.
Step 2: To calculate the x intercepts equate $f\left( x \right)=0$.
$\begin{align}
& \frac{x+2}{{{x}^{2}}+x-6}=0 \\
& x=-2
\end{align}$ ,
Step 3: To calculate the y intercepts evaluate $f\left( 0 \right)$.
$\begin{align}
& f\left( 0 \right)=\frac{2}{-6} \\
& f\left( 0 \right)=\frac{-1}{3} \\
\end{align}$
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.
$x=2,-3$
