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The image shows a table where various limits and function values must be evaluated using the graph of \( y = g(x) \). Let's go through each part step by step based on the graph:

### A. \( \lim_{x \to -3} g(x) \)
- From the graph, as \( x \) approaches \( -3 \) from both the left and right, the function values approach 1.
- **Answer: 1**

### B. \( \lim_{x \to -1} g(x) \)
- As \( x \) approaches \( -1 \) from both sides, the left limit approaches 4, but the right limit approaches -2.
- Since the left and right limits do not match, the limit does not exist.
- **Answer: Does not exist**

### C. \( \lim_{x \to -1^+} g(x) \)
- As \( x \) approaches \( -1 \) from the right, the function approaches -2.
- **Answer: -2**

### D. \( g(-1) \)
- The value of \( g(x) \) at \( x = -1 \) is marked by a filled circle at \( ( -1, -2 ) \), meaning \( g(-1) = -2 \).
- **Answer: -2**

### E. \( \lim_{x \to -1^-} g(x) \)
- As \( x \) approaches \( -1 \) from the left, the function approaches 4.
- **Answer: 4**

### F. \( \lim_{x \to 4^+} g(x) \)
- As \( x \) approaches 4 from the right, the function approaches \( -7 \).
- **Answer: -7**

### G. \( \lim_{x \to 4^-} g(x) \)
- As \( x \) approaches 4 from the left, the function approaches \( -2 \).
- **Answer: -2**

### H. \( \lim_{x \to 7} g(x) \)
- As \( x \) approaches 7 from both sides, the function approaches \( -7 \).
- **Answer: -7**

### J. \( g(7) \)
- The value of \( g(x) \) at \( x = 7 \) is marked by a filled circle at \( ( 7, -7 ) \), meaning \( g(7) = -7 \).
- **Answer: -7**

### K. \( \lim_{x \to 2^+} g(x) \)
- As \( x \) approaches 2 from the right, the function approaches \( -2 \).
- **Answer: -2**

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Would you like any further clarification or details?

Here are five related questions for practice:
1. What is \( \lim_{x \to 0} g(x) \) based on the graph?
2. How does the function behave as \( x \to -5 \)?
3. What is \( g(2) \) according to the graph?
4. Determine the left and right limits at \( x = 5 \).
5. What is the behavior of the graph as \( x \to 8 \)?

**Tip:** Always compare the left-hand and right-hand limits to check if the overall limit exists at a given point.

Use the graph of the function y = g(x) shown below, to evaluate each of the following limits and function values.

Evaluate various limits and function values using the graph of y = g(x). This problem covers important concepts such as one-sided limits and continuity. Suitable for students in Grades 10-12.

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