Answer
Center: $(0,1)$ $;$ Radius: $1$
Domain: $[-1,1]$ $;$ Range: $[0,2]$
The graph is:
Work Step by Step
$x^{2}+(y-1)^{2}=1$
The standard form of the equation of a circle is $(x-h)^{2}+(y-k)^{2}=r^{2}$, where $(h,k)$ is the center of the circle and $r$ is its radius.
From the equation given, it can be seen that $(h,k)=(0,1)$ and that $r^{2}=1$
The center of the circle is $(0,1)$
The radius of the circle is:
$r^{2}=1$
$\sqrt{r^{2}}=\sqrt{1}$
$r=1$
From the equation's graph (shown below), it can be seen that its domain is $[-1,1]$ and its range is $[0,2]$
