Answer
See graph and explanations.
Work Step by Step
Step 1. Given the function
$f(x)=\frac{x}{x^2-1}=\frac{x}{(x+1)(x-1)}$
we can identify two vertical asymptotes as $x=\pm1$
Step 2. We can identify a horizontal asymptote as $y=0$
Step 3. The x-intercept is $x=0$ and the y-intercept is $y=0$
Step 4. Testing signs across the vertical asymptotes and $x=0$, we have:
$...(-)...(-1)...(+)...(0)...(-)...(1)...(+)...$
Step 5. Testing for symmetry, $f(-x)=-f(x)$, the function is odd and symmetric with respect to the origin.
Step 6. Use the above results and test points if necessary to obtain a graph as shown in the figure.
