1. **Stating the problem:** We analyze the limits and vertical asymptotes of the function $A(x)$ given the behavior near $x = -3$, $x = 2$, and $x = -1$. 2. **Limits at vertical asymptotes:** Vertical asymptotes occur where the function tends to infinity or negative infinity as $x$ approaches a certain value. 3. **Given limits:** - $\lim_{x \to -3} A(x) = \infty$ - $\lim_{x \to 2^-} A(x) = -\infty$ - $\lim_{x \to 2^+} A(x) = \infty$ - $\lim_{x \to -1} A(x)$ does not exist (DNE) 4. **Vertical asymptotes:** From the problem, vertical asymptotes are at $x = -3$ and $x = 2$ where the function tends to $\pm \infty$. 5. **At $x = -1$:** The limit does not exist, so there is no vertical asymptote there. **Final answers:** - $\lim_{x \to -3} A(x) = \infty$ - $\lim_{x \to 2^-} A(x) = -\infty$ - $\lim_{x \to 2^+} A(x) = \infty$ - $\lim_{x \to -1} A(x) = \text{DNE}$ - Vertical asymptotes: $x = -3, 2$