https://file.aiquickdraw.com/mathbot/file/1726973619742twnllqoz.jpg

Based on the provided graph, it appears to represent a quadratic function. Let’s analyze the domain and range based on the visual characteristics of the graph.

### Domain:
The domain represents all possible \(x\)-values for which the function is defined. From the graph:
- The curve extends from \(x = -3\) to \(x = 3\), where both endpoints are marked with open circles. Open circles indicate that the function does not include those specific values.
  
Therefore, the **domain** is:
\[
(-3, 3)
\]
This means \(x\) can take any value between \(-3\) and \(3\), excluding \(-3\) and \(3\) themselves.

### Range:
The range represents all possible \(y\)-values for the function. From the graph:
- The lowest point is at \(y = -4\) (vertex of the parabola).
- The highest points are at \(y = 4\), but again, the open circles indicate that these points are not included.

Thus, the **range** is:
\[
[-4, 4)
\]
This means \(y\) can take any value between \(-4\) and just below \(4\), including \(-4\), but not 4 itself.

### Summary:
- **Domain:** \((-3, 3)\)
- **Range:** \([-4, 4)\)

Would you like more details or have any specific questions?

#### Related Questions:
1. How can I find the vertex of a parabola algebraically?
2. How do I determine if a function is continuous at its endpoints?
3. What are other methods to determine the range of a function?
4. Can a parabola have a restricted domain and range?
5. What happens to the domain and range if the graph includes the endpoints?

#### Tip:
Open circles on a graph mean the value is **excluded** at that point, while closed circles mean the value is **included**.

Discover how to find the domain and range of a quadratic function with excluded endpoints. This guide covers key mathematical concepts and provides a visual understanding of the function's behavior. Ideal for students in Grades 9-12.

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