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

Answer 1

[-6, 6]

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.

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Answer 2

Jameson Allen

Range: All real numbers such that y² ≤ 36.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.