# What is the range of the function x^2+y^2=36?

Apr 4, 2017

[-6, 6]

#### Explanation:

That relation is not a function.

The relation is in the standard form of a circle.
Its graph is a circle of radius 6 about the origin.
Its domain is [-6, 6], and its range is also [-6, 6].

To find this algebraically, solve for y.

${x}^{2} + {y}^{2} = 36$
${y}^{2} = 36 - {x}^{2}$
$y = \pm \sqrt{36 - {x}^{2}}$

The range is largest in absolute value when x = 0, and we have
$y = \pm \sqrt{36}$.
That is, at -6 and 6.