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can you tell me the domain and range in this graph

The graph shows a circle centered at the origin. To find the domain and range of the circle, we need to observe the radius and how the graph behaves along the \( x \)-axis (for the domain) and the \( y \)-axis (for the range).

### Domain:
The domain represents the set of all possible \( x \)-values for the points on the circle. Since the circle is centered at the origin and extends equally in both directions along the \( x \)-axis, the domain is limited by the radius.

From the graph, the circle appears to have a radius of 3 units. Thus, the \( x \)-values range from \( -3 \) to \( 3 \).

So, the domain is:
\[
\text{Domain}: [-3, 3]
\]

### Range:
The range represents the set of all possible \( y \)-values for the points on the circle. Similarly, the circle extends equally along the \( y \)-axis from \( -3 \) to \( 3 \).

So, the range is:
\[
\text{Range}: [-3, 3]
\]

Would you like more details or have any questions?

Here are 5 relative questions for you:
1. How would the domain and range change if the circle's radius was doubled?
2. Can you express the equation of this circle?
3. What is the area of this circle based on the graph?
4. How would the domain and range differ for an ellipse?
5. What would happen to the domain and range if the center of the circle was moved to \((2, 1)\)?

**Tip:** The domain refers to all possible \( x \)-values a function can take, and the range refers to all possible \( y \)-values.

Can you tell me the domain and range in this graph?

Understand how to determine the domain and range of a circle from its graph. Learn to use the equation of a circle and properties of the coordinate plane to find the correct domain and range. This problem involves key geometric concepts and is suitable for Grades 8-10.

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