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.
$x^{2}+y^{2}=81$
what is the center of the circle?
the circle is centered at the point (0,0).
(type an ordered pair.)
what is the radius of the circle?
the radius of the circle is 9.
(type an integer or a fraction.)
use the graphing tool to graph the circle.
what is the domain of the relation?
the domain is -9,9.
(type your answer in interval notation.)
what is the range of the relation?
the range is
(type your answer in interval notation.)

Explanation:

Step1: Recall circle - domain - range relationship

For a circle centered at the origin $(0,0)$ with radius $r$, the $x$ - values (domain) and $y$ - values (range) are bounded by $-r$ and $r$.

Step2: Identify the radius

The equation of the circle is $x^{2}+y^{2}=81$, which is in the form $x^{2}+y^{2}=r^{2}$, where $r^{2}=81$, so $r = 9$.

Step3: Determine the range

Since the circle is symmetric about the $x$ - axis and $y$ - axis and has a radius of 9, the minimum value of $y$ is $- 9$ and the maximum value of $y$ is 9.

Answer:

$[-9,9]$