# What is the domain and range of the function x^2+y^2 = 1?

Nov 14, 2017

Both domain and range is $\left[- 1 , + 1\right]$

#### Explanation:

The equation of a circle centred at point $\left(a , b\right)$ with radius $r$ is:
${\left(x - a\right)}^{2} + {\left(y - b\right)}^{2} = {r}^{2}$

$\therefore {x}^{2} + {y}^{2} = 1$ is the equation of a circle centred at the origin with radius 1.

Hence, domain and range are both $\left[- 1 , + 1\right]$

We can see this from the graph of ${x}^{2} + {y}^{2} = 1$ below.

graph{x^2+y^2=1 [-3.08, 3.08, -1.54, 1.54]}