Answer
The domain of ${{x}^{2}}+{{y}^{2}}=1$ is $\left[ -1,1 \right]$ and its range is $\left[ -1,1 \right]$.
Work Step by Step
Consider the provided equation:
${{x}^{2}}+{{y}^{2}}=1$
The provided equation can also be written as:
${{\left( x-0 \right)}^{2}}+{{\left( y-0 \right)}^{2}}={{\left( 1 \right)}^{2}}$
Now, this represents the standard equation of a circle with its center at $\left( 0,0 \right)$ and radius of $1$ unit.
For the domain:
The domain of a function means "all the possible values of x in the function".
Here in the graph, note that the values of x range between $-1$ and $1$, including these values.
So, the domain of the relation is $\left[ -1,1 \right]$
For the range:
The range of a function means "all the possible values of y in the function".
Here in the graph, note that the values of y range between $-1$ and $1$ including these values.
So, the range of the relation is $\left[ -1,1 \right]$
Therefore, the domain and range of the function are $\left[ -1,1 \right]$ and $\left[ -1,1 \right]$ respectively.
