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.
$(x + 4)^2 + (y - 3)^2 = 25$
the center is $(-4,3)$.
(type an ordered pair. simplify your answer.)
the radius is $5$.
(type an integer or a simplified fraction.)
graph the circle.
express the domain of the relation in interval notation.
$-9,1$
express the range of the relation in interval notation.
$\square$

Explanation:

Step1: Recall the formula for the range of a circle

The range of a circle \((x - h)^2+(y - k)^2=r^2\) is \([k - r,k + r]\). Here, \(k = 3\) and \(r = 5\).

Step2: Calculate the lower and upper bounds of the range

For the lower bound: \(k - r=3 - 5=-2\).
For the upper bound: \(k + r=3 + 5 = 8\).

Answer:

\([-2,8]\)