https://file.aiquickdraw.com/mathbot/file/1726458059190k8ixnfu8.jpg

Let's go through the information and solve the problem based on the graph provided.

### The problem asks you to find:

a. \( g(0) \)  
b. \( \lim_{x \to 0} g(x) \)  
c. \( g(1) \)  
d. \( \lim_{x \to -1} g(x) \)  

From the graph:

1. **For \( g(0) \)**:
   - Look at the value of \( g(x) \) when \( x = 0 \). The graph shows a point at \( (0, 2) \). So, \( g(0) = 2 \).

2. **For \( \lim_{x \to 0} g(x) \)**:
   - The limit as \( x \) approaches 0 is the value the function tends towards from both sides. Since the graph is continuous at \( x = 0 \) and the value at that point is 2, we have:
     \[
     \lim_{x \to 0} g(x) = 2
     \]

3. **For \( g(1) \)**:
   - Check the graph at \( x = 1 \). It shows the point at \( (1, 0) \), so \( g(1) = 0 \).

4. **For \( \lim_{x \to -1} g(x) \)**:
   - As \( x \to -1 \), the function approaches a value. The graph shows continuity around \( x = -1 \), and the value approaches 1. Hence:
     \[
     \lim_{x \to -1} g(x) = 1
     \]

### Summary:
- a. \( g(0) = 2 \)
- b. \( \lim_{x \to 0} g(x) = 2 \)
- c. \( g(1) = 0 \)
- d. \( \lim_{x \to -1} g(x) = 1 \)

Would you like to dive into any of these steps for more details? 

Here are 5 related questions you might find helpful:
1. What is the difference between a function value and a limit?
2. How do we evaluate limits from the left-hand and right-hand side of a point?
3. What happens when a function is not continuous at a point?
4. How do you interpret limits at infinity?
5. Can a function be undefined at a point but still have a limit?

**Tip:** Always check for continuity at the point when determining both the function's value and the limit.

Use the graph of g in the figure to find the following values: a. g(0), b. lim g(x) as x approaches 0, c. g(1), d. lim g(x) as x approaches -1.

Learn how to find function values and limits from a graph. This problem involves determining the value of g(0), g(1), and the limits as x approaches 0 and -1 using the continuity of the graph. Suitable for high school students in Calculus I.

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