# What is the range of the function x^2 + y^2 = 9?

Jan 4, 2018

The domain is $\left[- 3 , 3\right]$ and range too is $\left[- 3 , 3\right]$.

#### Explanation:

While domain depends on values that $x$ can take in $f \left(x , y\right) = 0$, range depends on values $y$ can take in $f \left(x , y\right)$.

In ${x}^{2} + {y}^{2} = 9$, as ${x}^{2}$ and ${y}^{2}$ both are positive and hence cannot take values beyond $9$.=,

the domain is $\left[- 3 , 3\right]$ and range too is $\left[- 3 , 3\right]$.