https://file.aiquickdraw.com/mathbot/file/1726842881850itoy3mu5.jpg

The image shows a circle centered at \( (2, 0) \) on a coordinate plane, with a radius of 3 units.

To find the domain, we focus on the \( x \)-coordinates covered by the circle. Since the circle is centered at \( (2, 0) \) and has a radius of 3, the \( x \)-coordinates will range from:

\[
2 - 3 = -1 \quad \text{to} \quad 2 + 3 = 5
\]

Thus, the domain of the circle is all \( x \)-values between \( -1 \) and \( 5 \), inclusive. In interval notation, the domain is:

\[
\boxed{[-1, 5]}
\]

Would you like more details or have any questions? Here are some related questions to consider:

1. What is the range of this circle?
2. How do you calculate the equation of this circle?
3. How does the radius affect the domain and range of a circle?
4. Can you generalize the domain for any circle centered at \( (h, k) \) with radius \( r \)?
5. How do transformations like shifting affect the domain of a circle?

**Tip:** When analyzing geometric shapes like circles, always keep the center and radius in mind to easily compute the domain and range.

What is the domain of the following circle shown on the coordinate plane?

Find the domain of a circle centered at (2, 0) with a radius of 3. Learn the steps to compute the x-values covered by the circle, focusing on coordinate geometry concepts and circle equations. Suitable for high school students in Grades 9-10.

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