Answer
Center: $(0, 0)$
Radius = 4
Domain: $[-4, 4]$
RangeL $[-4, 4]$
Refer to the image below for the graph.
Work Step by Step
RECALL:
The standard equation of a circle whose center is at $(h, k)$ and has a radius of $r$ units is:
$(x-h)^2 + (y-k)^2 = r^2$
Thus, using the standard form given above as guide, the given circle has:
Center: $(0, 0)$
Radius = $\sqrt{16} = 4$
To graph the circle, perform the following steps:
(1) Plot the center $(0, 0)$.
(2) From the center, plot the points 4 units to the center’s left, right, above, and below.
These points are $(-4, 0)$, $(4, 0)$, $(0, 4)$, and $(0, -4)$, respectively.
Connect these points using a curve to form a circle.
The domain is the set of x-values covered by the graph. Since the graph covers the x-values from -4 to 4, then the domain is:
$[-4, 4]$
The range is the set of y-values covered by the graph. Since the graph covers the y-values from -4 to 4, then the range is:
$[-4, 4]$
