1. **State the problem:** Find the vertical asymptotes of the function $$f(x) = \frac{3x - 7}{x^2 + 5x}$$. 2. **Recall the rule for vertical asymptotes:** Vertical asymptotes occur where the denominator is zero and the numerator is not zero at those points. 3. **Find the zeros of the denominator:** $$x^2 + 5x = x(x + 5) = 0$$ So, $$x = 0$$ or $$x = -5$$. 4. **Check the numerator at these points:** - At $$x=0$$, numerator $$3(0) - 7 = -7 \neq 0$$. - At $$x=-5$$, numerator $$3(-5) - 7 = -15 - 7 = -22 \neq 0$$. 5. **Conclusion:** Since the denominator is zero and numerator is not zero at $$x=0$$ and $$x=-5$$, vertical asymptotes are at $$x=0$$ and $$x=-5$$. 6. **Compare with options:** The correct vertical asymptotes are at $$x=0$$ and $$x=-5$$, but option b says $$x=0$$ and $$x=5$$ which is incorrect. 7. **Final answer:** None of the options exactly match the correct vertical asymptotes. **Answer:** e. none of the above