Question

give the center and radius of the circle described by the equation and graph the equation. use the graph to identify the domain and range.
$(x + 3)^{2}+(y - 1)^{2}=9$
the center is $(-3,1)$
(type an ordered pair. simplify your answer.)
the radius is 3
(type an integer or a simplified fraction.)
graph the circle.
express the domain of the relation in interval notation.

Explanation:

Step1: Recall the domain formula for a circle

For a circle \((x - h)^2+(y - k)^2=r^2\), the domain is \([h - r,h + r]\). Here \(h=-3\) and \(r = 3\).

Step2: Calculate the domain interval

Substitute \(h=-3\) and \(r = 3\) into the formula. \(h - r=-3-3=-6\) and \(h + r=-3 + 3=0\).

Answer:

\([-6,0]\)