https://file.aiquickdraw.com/mathbot/file/1726236553392viix51vu.jpg

The graph in the image shows a curve resembling a semi-circle, with the open circle indicating that it does not include the endpoint at the top. Let's address the three parts of the question:

1. **Domain**: The domain refers to the x-values for which the graph exists. From the graph, the curve spans from \( x = -4 \) to \( x = 4 \). Since the graph includes both endpoints, the domain is:
   \[
   [-4, 4]
   \]

2. **Range**: The range refers to the y-values that the graph takes. The graph exists from \( y = -4 \) to \( y = 0 \), but since the top part of the graph (y = 0) has an open circle, the range does not include \( y = 0 \). Thus, the range is:
   \[
   [-4, 0)
   \]
   The parenthesis indicates that 0 is not included in the range.

3. **Function?**: To determine if the graph represents a function, we apply the **vertical line test**. If any vertical line intersects the graph more than once, it is not a function. Here, several vertical lines would intersect the graph twice (once on each side of the semi-circle), so **this graph is not a function**. The correct answer is "no."

### Summary of answers:
- **Domain**: \([-4, 4]\)
- **Range**: \([-4, 0)\)
- **Function?**: No

Do you want more details or have any questions?

Here are 5 related questions you can consider:
1. How do you determine the domain and range for different types of functions?
2. What is the vertical line test, and how can you use it to determine if a graph is a function?
3. How would the domain and range change if the circle at the top of the graph was filled in?
4. What are some examples of graphs that pass the vertical line test?
5. How can you modify a semi-circle graph so that it represents a function?

**Tip**: When determining if a graph represents a function, always visualize or use the vertical line test to ensure each x-value corresponds to only one y-value.

Determine the domain, range, and if the given graph represents a function. Express answers in interval notation where applicable.

This problem involves analyzing the domain and range of a semi-circle graph and determining whether the graph represents a function using the vertical line test. Ideal for students in Grades 9-10.

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