Answer
Graph the function as:
Work Step by Step
Step 1: Substitute $x=-x$
$\begin{align}
& f\left( x \right)=\frac{-1}{{{x}^{2}}-4} \\
& f\left( -x \right)=\frac{-1}{{{\left( -x \right)}^{2}}-4} \\
& =\frac{-1}{{{x}^{2}}-4} \\
& =f\left( x \right)
\end{align}$
Therefore, the function $f\left( -x \right)$ is equal to $f\left( x \right)$. So, the graph of the function is symmetrical about the $y$-axis and origin.
There are no x-intercepts.
Step 2: To calculate the y intercepts, evaluate $f\left( 0 \right)$
$\begin{align}
& f\left( 0 \right)=\frac{-1}{\left( 0 \right)-4} \\
& f\left( 0 \right)=\frac{1}{4} \\
\end{align}$
Step 3: Since the degree of the numerator is less than the denominator, there is no horizontal asymptote.
Step 4: For the vertical asymptote, equate the denominator to 0.
$\begin{align}
& x-1=0 \\
& x=1
\end{align}$
