#### Answer

no vertical asymptote.
no horizontal asymptote.
slant asymptote: $y=-2x$
See graph.

#### Work Step by Step

Step 1. Rewrite the function as
$f(x)=\frac{-2x^3}{x^2+1}=\frac{-2x^3-2x+2x}{x^2+1}=-2x+\frac{2x}{x^2+1}$
Step 2. There is no vertical asymptote.
Step 3. There is no horizontal asymptote.
Step 4. A slant asymptote can be found as $y=-2x$
Step 5. See graph.