In Exercises 41–52, give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation's domain and range. (x + 2)² + (y - 2)² = 4

Key Concepts

Equation of a Circle

The standard form of the equation of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius. In the given equation, (x + 2)² + (y - 2)² = 4, we can identify the center as (-2, 2) and the radius as 2, since r² = 4 implies r = 2.

Graphing Circles

To graph a circle, plot the center point on the coordinate plane and use the radius to mark points in all directions (up, down, left, right) from the center. The resulting shape is a circle, and understanding how to accurately represent this visually is crucial for analyzing the relation's domain and range.

Domain and Range

The domain of a relation refers to all possible x-values, while the range refers to all possible y-values. For the circle described, the domain is the interval [-4, 0] and the range is [0, 4], as these values encompass the horizontal and vertical extents of the circle based on its center and radius.