https://file.aiquickdraw.com/mathbot/file/1727758019864m4psfs4c.jpg

Let's analyze the problem and graph in your image step by step:

The question asks you to:

1. **Find the domain and range of g**.
2. **Use the formula to evaluate** \( g(-2) \) and \( g(2) \).
3. **Use the graph to evaluate** \( g(-2) \) and \( g(2) \).
4. Find the domain of \( g \) based on a given interval or notation choice.

From the graph provided:

- The **domain** of \( g(x) \) refers to the set of all possible input values (x-values) where the graph is defined.
  - The graph seems to have endpoints at \( x = -4 \) and \( x = 4 \), meaning the domain is \( [-4, 4] \).
  
- The **range** of \( g(x) \) is the set of all possible output values (y-values) that the function can take.
  - By looking at the highest and lowest points of the graph, the range appears to be between \( y = -2 \) and \( y = 3 \), so the range is \( [-2, 3] \).

For parts b and c:

- **To evaluate** \( g(-2) \) and \( g(2) \), simply locate these values on the graph.
  - At \( x = -2 \), the y-value on the graph is \( 1 \), so \( g(-2) = 1 \).
  - At \( x = 2 \), the y-value is \( -1 \), so \( g(2) = -1 \).

Now for the multiple-choice part, select the domain based on the answer choices provided in the exercise (likely \( [-4, 4] \)).

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Would you like to go over more details, or do you have any other questions about this?

Here are 5 follow-up questions for further exploration:
1. Can you describe the meaning of "range" in your own words?
2. What other methods can be used to find the range of a function?
3. What is the difference between discrete and continuous domains?
4. How does the shape of a graph influence its domain and range?
5. How would you determine \( g(x) \) values if the graph were not provided?

**Tip**: Always check the endpoints on a graph carefully to define the domain and range correctly.

Use the graph to find the domain and range of g(x), evaluate g(-2) and g(2), and determine the correct domain notation for g.

Learn how to find the domain and range of a function from its graph, and evaluate specific points such as g(-2) and g(2). Suitable for students in Grades 9-11.

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