Give the center and radius of the circle described by the equation and graph the equation. Use the graph to identify the relation's domain and range. \[ x^{2}+y^{2}=1 \]

The equation \( x^{2}+y^{2}=1 \) represents a circle centered at the origin (0, 0) with a radius of 1. This means every point on the circle is exactly 1 unit away from the center. When graphed, the circle will be symmetric about both the x-axis and the y-axis. The domain of this relation is all x-values from -1 to 1 (i.e., \([-1, 1]\)), while the range is all y-values from -1 to 1 (i.e., \([-1, 1]\)) as well, since the circle does not extend beyond these limits in any direction.