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To determine the domain and range of the function represented by the graph, let's analyze the endpoints and behavior of the graph:

### Domain:
The domain represents the set of all possible \( x \)-values for which the function is defined.

- The graph starts at \( x = -2 \) on the left (open circle, meaning \( x = -2 \) is not included).
- The graph extends to \( x = 3 \) on the right (closed circle, meaning \( x = 3 \) is included).
- Therefore, the domain is \( -2 \leq x \leq 3 \).

### Range:
The range represents the set of all possible \( y \)-values that the function takes.

- The graph starts at \( y = -2 \) (open circle, meaning \( y = -2 \) is not included).
- The graph extends to \( y = 4 \) (closed circle, meaning \( y = 4 \) is included).
- Therefore, the range is \( -2 < y \leq 4 \).

Now, let's look at the answer choices:
- **Option D: \( -2 \leq x \leq 3 \) and \( -1 \leq y \leq 4 \)** doesn't include the lower bound correctly for the \( y \)-values.
- **Option A: \( -2 \leq x \leq 3 \) and \( -2 \leq y \leq 4 \)** matches the description, except the inequality \( y = -2 \) is incorrect because it's an open circle at \( y = -2 \).

Thus, **the correct answer is Option A**.

Would you like any additional details or clarifications?

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Here are 5 related questions:
1. What is the definition of domain and range in general?
2. How do you interpret open and closed circles on a graph?
3. What are other methods for finding the range of a function?
4. How does one determine if a function is continuous from its graph?
5. Can a function have a different domain than range?

**Tip:** Always check the endpoints of a graph carefully to see whether the points are included (closed circle) or excluded (open circle).

Select the domain and range of the function represented by the graph.

Learn how to determine the domain and range from a function graph. This example illustrates the use of open and closed circles, inequalities, and proper analysis of graph endpoints. Suitable for Grades 8-10.

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