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.