Question

give the center and radius of the circle described by the equation and graph the equation. use the graph to identify the relations domain and range.

what is the center of the circle?
the circle is centered at the point (0,1).
(type an ordered pair.)
what is the radius of the circle?
the radius of the circle is 4.
(type an integer or a fraction.)
use the graphing tool to graph the circle.

what is the domain?
the domain is -4,4.
(type your answer in interval notation.)
what is the range?
the range is □
(type your answer in interval notation.)

Explanation:

Step1: Recall the standard form of a circle equation

The standard form of a circle equation is \((x - h)^2+(y - k)^2=r^2\), where \((h,k)\) is the center and \(r\) is the radius. For the given equation \(x^{2}+(y - 1)^{2}=16\), we have \(h = 0\), \(k=1\), and \(r^{2}=16\).

Step2: Find the range

The \(y\) - coordinate of the center is \(k = 1\) and the radius \(r = 4\). The minimum value of \(y\) is \(k-r=1 - 4=-3\) and the maximum value of \(y\) is \(k + r=1+4 = 5\).

Answer:

The range is \([-3,5]\)