Let's analyze the graph and the questions presented:

1. Limit as $x \to \infty$ (Question a):

   • We need to find $\lim_{x \to \infty} f(x)$, meaning what happens to the function $f(x)$ as $x$ approaches positive infinity. From the graph, as $x$ increases to large positive values, the function appears to approach the horizontal line $y = 0$, so the limit is 0.

2. Limit as $x \to -\infty$ (Question b):

   • Similarly, for $\lim_{x \to -\infty} f(x)$, as $x$ becomes very negative, the function also seems to approach the horizontal line $y = 0$. Thus, the limit is 0.

3. Limit as $x \to 1$ (Question c):

   • Around $x = 1$, the graph shows a vertical asymptote. As $x$ approaches 1 from either side, the function tends to $\infty$ or $-\infty$, indicating the function has no limit and tends to infinity.

4. Limit as $x \to 3$ (Question d):

   • At $x = 3$, the graph does not show any discontinuity, and the function seems to approach a specific value. Based on the graph, $\lim_{x \to 3} f(x)$ appears to be about -1.

5. Asymptotes (Question e):

   • Vertical asymptote: From the graph, there is a vertical asymptote at $x = 1$.
   • Horizontal asymptote: The function approaches the horizontal line $y = 0$ as $x \to \infty$ or $x \to -\infty$, so the horizontal asymptote is $y = 0$.

Answers:

• (a) $\lim_{x \to \infty} f(x) = 0$
• (b) $\lim_{x \to -\infty} f(x) = 0$
• (c) $\lim_{x \to 1} f(x) = \infty$
• (d) $\lim_{x \to 3} f(x) = -1$
• (e) Vertical asymptote: $x = 1$, Horizontal asymptote: $y = 0$

Would you like further details on any part? Here are five questions that can deepen your understanding:

1. Why does the function have no limit at $x = 1$?
2. What is the difference between vertical and horizontal asymptotes?
3. How can you tell if a graph approaches a specific value as $x \to \infty$?
4. Why does the limit at $x = 3$ exist and equal -1, unlike at $x = 1$?
5. What are common behaviors of functions around vertical asymptotes?

Tip: When determining limits graphically, watch for asymptotes and the general trend of the function's behavior.