I have displayed the image you uploaded. Let's analyze the graph and questions.

We are asked to find:

1. $\lim_{x \to 3^-} f(x)$
2. $\lim_{x \to 3^+} f(x)$
3. $\lim_{x \to 3} f(x)$
4. $f(3)$

Let's break it down:

• The limit as $x \to 3^-$ asks for the value the function approaches as $x$ gets close to 3 from the left.
• The limit as $x \to 3^+$ asks for the value as $x$ gets close to 3 from the right.
• The overall limit $\lim_{x \to 3} f(x)$ exists if both the left-hand and right-hand limits are equal.
• Finally, $f(3)$ refers to the actual value of the function at $x = 3$.

Observations from the graph:

• As $x \to 3^-$, it seems that $f(x)$ approaches $2$.
• As $x \to 3^+$, the graph of $f(x)$ also appears to approach $2$.
• Since the left-hand and right-hand limits are the same, $\lim_{x \to 3} f(x) = 2$.
• At $x = 3$, there is a hole in the graph, meaning $f(3)$ is undefined.

Answers:

1. $\lim_{x \to 3^-} f(x) = 2$
2. $\lim_{x \to 3^+} f(x) = 2$
3. $\lim_{x \to 3} f(x) = 2$
4. $f(3)$ is undefined (or does not exist).

Would you like more details or have any other questions?

Here are 5 related questions:

1. What is the difference between a limit and the value of a function at a point?
2. How can discontinuities affect limits and function values?
3. Can a function have a limit at a point where it is not defined?
4. How do you interpret infinite limits from a graph?
5. What are jump discontinuities, and how are they related to limits?

Tip: When limits from the left and right at a point are different, the overall limit does not exist at that point.