Let's solve the problem based on the information provided:

The problem involves evaluating certain values and limits from the graph of $f(x)$ shown in Figure 13.

1. $f(-3)$:

   • From the graph, at $x = -3$, there is a filled dot at $y = -2$.
   • Therefore, $f(-3) = -2$.

2. $f(3)$:

   • At $x = 3$, there is an open circle at $y = 1$, meaning $f(3)$ does not exist since there’s no defined value at that point.
   • So, $f(3)$ does not exist.

3. $\lim_{x \to -3^+} f(x)$:

   • As $x$ approaches $-3$ from the right, the function value approaches $y = 1$.
   • Thus, $\lim_{x \to -3^+} f(x) = 1$.

4. $\lim_{x \to -3^-} f(x)$:

   • As $x$ approaches $-3$ from the left, the function value approaches $y = -2$.
   • Therefore, $\lim_{x \to -3^-} f(x) = -2$.

5. $\lim_{x \to -3} f(x)$:

   • Since $\lim_{x \to -3^+} f(x) \neq \lim_{x \to -3^-} f(x)$, the two-sided limit $\lim_{x \to -3} f(x)$ does not exist.

6. $\lim_{x \to 3} f(x)$:

   • As $x$ approaches $3$ from both the left and the right, $f(x)$ approaches $y = 1$.
   • Thus, $\lim_{x \to 3} f(x) = 1$.

Summary of Results:

• (a) $f(-3) = -2$
• (b) $f(3)$ does not exist
• (c) $\lim_{x \to -3^+} f(x) = 1$
• (d) $\lim_{x \to -3^-} f(x) = -2$
• (e) $\lim_{x \to -3} f(x)$ does not exist
• (f) $\lim_{x \to 3} f(x) = 1$

Would you like a more detailed explanation of any of these answers?

Here are five related questions to deepen your understanding:

1. How does the existence of open or closed circles at certain points affect the limits and function values?
2. Why does the limit at $x = -3$ not exist if the left- and right-hand limits differ?
3. How do you determine one-sided limits by looking at a graph?
4. What is the significance of a function value not existing at a certain point, as in $f(3)$?
5. How would the answer change if there were a closed dot at $x = 3$ on the graph?

Tip: When evaluating limits graphically, always check both the left-hand and right-hand behavior as $x$ approaches the point of interest.