https://file.aiquickdraw.com/mathbot/file/1729995264564b6y9wgv0.jpg

This graph shows an ellipse centered at the origin \((0,0)\).

To determine the **domain** and **range**:

### Domain:
The domain represents the possible \( x \)-values.
- From the graph, the ellipse extends horizontally from \( x = -5 \) to \( x = 5 \).
- Therefore, the domain is:
  \[
  -5 \leq x \leq 5
  \]

### Range:
The range represents the possible \( y \)-values.
- The ellipse extends vertically from \( y = -3 \) to \( y = 3 \).
- Thus, the range is:
  \[
  -3 \leq y \leq 3
  \]

### Summary:
- **Domain**: \([-5, 5]\)
- **Range**: \([-3, 3]\)

Would you like more details on how to find these values or further questions? 

Here are some follow-up questions:
1. What is the equation of this ellipse?
2. How would the domain and range change if the ellipse were moved?
3. What if the axes were stretched or compressed—how would that impact domain and range?
4. How is the length of the major and minor axis determined?
5. What if we rotated the ellipse—would the domain and range change?

**Tip:** The center of an ellipse provides a quick reference to split the domain and range equally along each axis.

Determine the domain and range for the ellipse shown in the graph.

Explore how to find the domain and range of an ellipse centered at the origin, with a detailed solution and key geometry concepts. This example demonstrates the ellipse's properties, suitable for high school students studying coordinate geometry.

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