Question

1. domain: ( ) ( ) range: ( ) ( )

Explanation:

Step1: Identify circle equation form

The general form of a circle centered at the origin $(0,0)$ is $x^{2}+y^{2}=r^{2}$. For a circle, the domain is the set of all possible $x -$ values and the range is the set of all possible $y -$ values.

Step2: Determine domain

If the radius of the circle is $r$, from the equation $x^{2}+y^{2}=r^{2}$, we can solve for $x$: $x=\pm\sqrt{r^{2}-y^{2}}$. The left - most and right - most points of the circle give the bounds of the domain. If we assume the radius of the circle is 3 (by counting the grid units from the center to the edge of the circle), then $x$ ranges from $- 3$ to $3$. So the domain is $[-3,3]$.

Step3: Determine range

Similarly, solving the circle equation $x^{2}+y^{2}=r^{2}$ for $y$ gives $y = \pm\sqrt{r^{2}-x^{2}}$. The bottom - most and top - most points of the circle give the bounds of the range. With radius $r = 3$, $y$ ranges from $-3$ to $3$. So the range is $[-3,3]$.

Answer:

Domain: $[-3,3]$, Range: $[-3,3]$