Answer
Graph the function as:
Work Step by Step
Step 1: Substitute $x=-x.$
$\begin{align}
& f\left( x \right)=\frac{x-3}{{{x}^{2}}-9} \\
& f\left( -x \right)=\frac{\left( -x \right)-3}{{{\left( -x \right)}^{2}}-9} \\
& =\frac{-x-3}{{{x}^{2}}-9} \\
& \ne -f\left( x \right)
\end{align}$
Therefore, the function $f\left( -x \right)$ is not equal to $-f\left( x \right)$ and the function $f\left( x \right)$. The graph of the function is not symmetric about $y\text{-}$ axis and origin.
Step 2: To calculate the x intercepts equate $f\left( x \right)=0$.
There are no values of x for which the equation holds true, hence there are no x intercepts.
Step 3: To calculate the y intercepts evaluate $f\left( 0 \right)$.
$f\left( 0 \right)=\frac{1}{3}$
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.
$x=-3$
