https://file.aiquickdraw.com/mathbot/file/172568019184521lwlu8x.jpg

To solve the problem, let's analyze the information given in the image:

The question asks for the domain of the function based on the graph provided. The domain of a function represents all the possible input values (usually \(x\)-values) for which the function is defined.

### Observations from the Graph
From the graph:
1. The function seems to have two vertical asymptotes where the function is not defined.
2. These vertical asymptotes are around \(x = -3\) and \(x = 2\).

### Domain of the Function
Given the asymptotes, the function is undefined at these points. Therefore, the domain will include all \(x\) values except \(x = -3\) and \(x = 2\).

### Possible Answers
- **D = (X/-3≤X≤2):** This notation suggests that the domain is between \(-3\) and \(2\), but includes the endpoints \(-3\) and \(2\). However, since the function is not defined at these points, this cannot be the correct answer.
- **D = (X/-3≠X≠2):** This is the correct answer. It indicates that \(x\) can take any value except \(-3\) and \(2\).

### Conclusion
The correct choice for the domain of the function, given the graph, is:

**D = (X/-3≠X≠2)**.

Would you like more details on this topic or have any questions?

Here are some related questions that could help expand your understanding:

1. What are vertical asymptotes and how do they affect the domain of a function?
2. How do we determine the range of a function from its graph?
3. What is the significance of the x-intercepts and y-intercepts in determining the properties of a function?
4. How do you find the domain and range of a function algebraically?
5. What are common types of discontinuities in functions, and how do they affect the graph?

**Tip:** To determine the domain from a graph, always check for vertical asymptotes, holes, and any other points where the function is not defined.

What is the domain of the function given the graph?

Learn how to determine the domain of a function by analyzing its graph. This example focuses on vertical asymptotes and how they affect the domain. Suitable for students in Grades 10-12.

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