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