Decoding the Mysteries of the Translated Circle: Unveiling the Domain and Range of (x – 2)² + (y + 1)² = 1

The equation (x – 2)² + (y + 1)² = 1 represents a circle with a radius of 1, centered at the point (2, -1) in the Cartesian coordinate system.

Domain

The domain of the equation is the set of all possible x-values that make the equation true. For this circle, x can range from 1 to 3, inclusive. Mathematically, the domain is: 1 ≤ x ≤ 3.

Range

The range of the equation is the set of all possible y-values that make the equation true. For this circle, y can range from -2 to 0, inclusive. Mathematically, the range is: -2 ≤ y ≤ 0.

Conclusion

The domain and range of (x – 2)² + (y + 1)² = 1 are 1 ≤ x ≤ 3 and -2 ≤ y ≤ 0, respectively. These values are derived from the geometric properties of the circle, specifically its radius and center.