vertical asymptotes $x\pm3$ horizontal asymptote $y=0$ no slant asymptote. See graph.
Work Step by Step
Step 1. The vertical asymptotes can be found by letting $x^2-9=0$, which gives $x\pm3$ Step 2. The horizontal asymptote can be found when $x\pm\infty$ and we get $y=0$ Step 3. The slant asymptotes exist if the numerator is one order higher than the denominator; for the given rational function, there is no slant asymptote. Step 4. See graph.