Answer
See graph and explanations.
Work Step by Step
Step 1. Given $f(x)=\frac{x^2-1}{x^2-9}=\frac{(x+1)(x-1)}{(x+3)(x-3)}$, we have $f(-x)=\frac{(-x)^2-1}{(-x)^2-9}=\frac{x^2-1}{x^2-9}=f(x)$, symmetric around the y-axis.
Step 2. Vertical asymptote: $x=\pm3$
Step 3. Horizontal asymptote: $y=1$
Step 4. X-intercept: $x=\pm1$
Step 5. Y-intercept: $f(0)=\frac{1}{9}$
Step 6. Use test points as necessary to graph the function as shown.
