Answer
See graph and explanations.
Work Step by Step
Step 1. Factor the denominator, we have $f(x)=\frac{3x+1}{(x+5)(x+2)}$
Step 2. We can identify two vertical asymptotes as $x=-5$ and $x=-2$
Step 3. The horizontal asymptote is $y=0$
Step 4. The x-intercept is $x=-\frac{1}{3}$
Step 5. The y-intercept is $y=\frac{1}{10}$
Step 6. Use test points as necessary to graph the function as shown in the figure.