Question

graph 8
(graph of a circle on a coordinate grid)
domain:
place domain of graph here
range:
place range of graph here

Explanation:

Step1: Identify the center and radius

The graph is a circle centered at \((0, 2)\) (since it's on the y - axis, 2 units above the x - axis) with a radius of 3 (by counting the grid squares from the center to the edge of the circle).

Step2: Find the domain

The domain of a circle is the set of all x - values. For a circle with center \((h,k)\) and radius \(r\), the domain is \(h - r\leq x\leq h + r\). Here, \(h = 0\) and \(r=3\), so the domain is \(- 3\leq x\leq3\) or in interval notation \([-3,3]\).

Step3: Find the range

The range of a circle is the set of all y - values. Using the formula for the range of a circle \(k - r\leq y\leq k + r\), with \(k = 2\) and \(r = 3\), we get \(2-3\leq y\leq2 + 3\), which simplifies to \(-1\leq y\leq5\) or in interval notation \([-1,5]\).

Answer:

Domain: \([-3, 3]\)
Range: \([-1, 5]\)