https://file.aiquickdraw.com/mathbot/file/1725514606046wgehuj1n.jpg

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.

Answer all of the questions below about the function f(x) graphed below when x = 3.

Analyze the graph of f(x) and find the left-hand limit, right-hand limit, overall limit, and the value of the function at x = 3. Learn how to approach limits and understand function discontinuities through this detailed solution.

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