https://file.aiquickdraw.com/mathbot/file/17272378193796q2f9tqy.jpg

Let's analyze the graph and the given questions regarding the limits.

1. **\( \lim_{x \to 2^-} g(x) = 1 \)**:
   - Looking at the graph from the left-hand side of \( x = 2 \), as \( x \) approaches 2, the function approaches the value 1. So, this limit is correct.

2. **\( \lim_{x \to 2^+} g(x) = 5 \)**:
   - From the right-hand side of \( x = 2 \), as \( x \) approaches 2, the function value approaches 5. This limit is also correct.

3. **\( \lim_{x \to 2} g(x) = \text{DNE} \)** (Does Not Exist):
   - Since the left-hand limit (\( 1 \)) and the right-hand limit (\( 5 \)) are not equal, the overall limit at \( x = 2 \) does not exist. This answer is correct.

4. **\( \lim_{x \to 0} g(x) = -3 \)**:
   - As \( x \) approaches 0, the function value approaches \( -3 \). So, this is correct.

5. **\( g(2) = 1 \)**:
   - The graph shows that there is a closed dot at \( x = 2 \) and \( g(2) = 1 \), indicating that the function value at \( x = 2 \) is indeed 1. This is correct.

### Summary:
- All the answers provided are correct based on the graph.

Would you like more details on any of these limit properties or explanations on one-sided limits and discontinuities?

### Related Questions:
1. What is the difference between one-sided and two-sided limits?
2. Why does the overall limit not exist if the one-sided limits are unequal?
3. How do you determine if a function is continuous at a point?
4. What are jump discontinuities, and how can they be identified on a graph?
5. Can a function have a value at a point where the limit does not exist?

### Tip:
Always check both one-sided limits when evaluating the overall limit at a point of discontinuity.

Use the given graph of the function g to find the following limits:
1. lim(x -> 2^-) g(x)
2. lim(x -> 2^+) g(x)
3. lim(x -> 2) g(x)
4. lim(x -> 0) g(x)
5. g(2)

Analyze a graph of the function g to find the left-hand and right-hand limits at x=2, evaluate the overall limit at x=2, and determine the value of the function at specific points. This problem focuses on understanding one-sided limits and discontinuities, suitable for students in Grades 11-12.

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