Answer
Graph the function as:
Work Step by Step
Step 1: Substitute $x=-x$
$\begin{align}
& f\left( x \right)=\frac{-x}{x+1} \\
& f\left( -x \right)=\frac{-\left( -x \right)}{\left( -x \right)+1} \\
& =\frac{x}{-x+1}
\end{align}$
Therefore, the function $f\left( -x \right)$ is not equal to either $f\left( x \right)$ or $-f\left( x \right)$. So, the graph of the function is neither symmetrical about the $y$ axis nor origin.
Step 2: To calculate the x intercepts equate $f\left( x \right)=0$.
$\begin{align}
& \frac{-x}{x+1}=0 \\
& x=0
\end{align}$
Step 3: To calculate the y intercepts, evaluate $f\left( 0 \right)$
$\begin{align}
& f\left( 0 \right)=\frac{-\left( 0 \right)}{\left( 0 \right)+1} \\
& f\left( 0 \right)=0 \\
\end{align}$
Step 4: Since the degree of the numerator is equal to the denominator, the horizontal asymptote is:
$y=-1$.
Step 5: For the vertical asymptote, equate the denominator to 0.
$\begin{align}
& x+1=0 \\
& x=-1
\end{align}$
