Answer
See graph and explanations.
Work Step by Step
Step 1. As $f(-x)=f(x)$, the function is even and symmetric with respect to the y-axis.
Step 2. The denominator is $x^2-9=(x+3)(x-3)$; the function has vertical asymptotes $x=\pm3$
Step 3. As $x\to\pm\infty, y\to4$, the function has a horizontal asymptote $y=4$
Step 4. The x-intercept can be found as $x=0$
Step 5. The y-intercept can be found as $y=0$
Step 6. The signs of the function across boundary points $x=\pm3$ are $...(+)...(-3)...(-)...(3)...(+)...$
Step 7. Based on the above information, we can graph the function as shown in the figure.
