vertical asymptote $x=-3$ horizontal asymptote $y=2$ no slant asymptote. See graph.
Work Step by Step
Step 1. The vertical asymptotes can be found by letting $x+3=0$, which gives $x=-3$ Step 2. The horizontal asymptote can be found when $x\pm\infty$ and we get $y=2$ Step 3. A slant asymptote exists if the numerator is one order higher than the denominator; for the given rational function, there is no slant asymptote. Step 4. See graph.