https://file.aiquickdraw.com/mathbot/file/1725386071274yc6cd8iv.jpg

The image provided shows the graph of a linear function with endpoints.

### To find:
1. **Domain**: The set of all possible x-values (inputs) for which the function is defined.
2. **Range**: The set of all possible y-values (outputs) the function can take.

### Graph Analysis:
- The function is linear, meaning it's a straight line.
- From the image, the line segment has two endpoints: one is at approximately (-9, 9), and the other at (4, 5).

### 1. **Domain**:
The domain of the function is the horizontal span of the line segment. The x-values range from:
- \( x = -9 \) to \( x = 4 \).

Thus, the domain is:
\[
\boxed{[-9, 4]}
\]

### 2. **Range**:
The range of the function is the vertical span of the line segment. The y-values range from:
- \( y = 5 \) to \( y = 9 \).

Thus, the range is:
\[
\boxed{[5, 9]}
\]

### Conclusion:
- **Domain**: \( [-9, 4] \)
- **Range**: \( [5, 9] \)

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Would you like more details on how these were calculated, or do you have any questions about this graph?

Here are some relative questions to expand your understanding:

1. How do you determine the slope of a line from two points?
2. What is the difference between the domain and the range of a function?
3. How can we find the equation of a linear function from two points on the graph?
4. How do restrictions on domain affect the behavior of the function?
5. What are other ways to represent the domain and range of a function?

**Tip**: Always check the endpoints carefully to determine if the domain and range are inclusive (closed intervals) or not (open intervals).

What are the domain and range of the linear function shown in the graph?

Learn how to determine the domain and range of a linear function by analyzing the graph. This example uses a function with endpoints at approximately (-9, 9) and (4, 5) to illustrate the process. Suitable for students in Grades 8-10.

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