https://file.aiquickdraw.com/mathbot/file/1726662890704nagumvbc.jpg

Let's go through the problem based on the graph you provided:

### The graph represents \( y = g(x) \), and you need to find the following:

#### a) \( g(0) \)
Look for where \( x = 0 \) on the graph. The corresponding value of \( y \) at \( x = 0 \) is approximately 1.

So, \( g(0) = 1 \).

#### b) \( g(-1) \)
Look for where \( x = -1 \) on the graph. The corresponding value of \( y \) at \( x = -1 \) is approximately 0.

So, \( g(-1) = 0 \).

#### c) The domain
The domain represents all the possible values of \( x \). From the graph, the function appears to be defined for all \( x \) between -5 and 3 (inclusive), so:

The domain is \( [-5, 3] \).

#### d) The range
The range represents all the possible values of \( y \). From the graph, the lowest point is \( y = -5 \) and the highest point is \( y = 3 \). Thus:

The range is \( [-5, 3] \).

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### Summary of the answers:
- a) \( g(0) = 1 \)
- b) \( g(-1) = 0 \)
- c) Domain: \( [-5, 3] \)
- d) Range: \( [-5, 3] \)

Would you like more details on any part of this? Here are some related questions to expand your understanding:

1. How do you determine the domain of a function from its graph?
2. What is the process for finding a function's range from a graph?
3. How would the answers change if the graph had open endpoints?
4. What are some real-world examples where functions like this might apply?
5. How can you use transformations to modify the graph of \( g(x) \)?

**Tip:** Always check if there are any breaks or holes in a graph when determining the domain and range.

Use the graph of y = g(x) to find: a) g(0), b) g(-1), c) The domain, d) The range.

Learn how to interpret the graph of a function y = g(x) to find key values such as g(0) and g(-1), and determine its domain and range. This problem focuses on graph interpretation, function evaluation, and understanding domains and ranges. Suitable for students in Grades 9-11.

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