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. x² + y² = 16

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 x² + y² = 16, it can be rewritten as (x - 0)² + (y - 0)² = 4², indicating that the center is at (0, 0) and the radius is 4.

Graphing Circles

To graph a circle, plot the center point and use the radius to mark points in all directions (up, down, left, right) from the center. The resulting shape is a round figure where all points are equidistant from the center, allowing for a visual representation of the circle's equation.

Domain and Range

The domain of a function refers to all possible x-values, while the range refers to all possible y-values. For the circle described by x² + y² = 16, the domain is [-4, 4] and the range is also [-4, 4], as the circle is centered at the origin and extends 4 units in all directions.