Question

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

Answer 1

[-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 = +- sqrt(36 - x^2)`

The range is largest in absolute value when x = 0, and we have
`y = +- sqrt(36)`.
That is, at -6 and 6.