How do you find the domain and range for y =sqrt(9-x^2)?

1 Answer
Alan P.
Feb 18, 2016

Domain: x in [-3,+3]
Range: yin [0,3]

Explanation:

I assume that we are dealing only with Real numbers.

For Real numbers sqrt(a) is only defined if a>=0
rarr (9-x^2)>=0
rarr abs(x)<=3
which gives us the Domain.

The maximum value of sqrt(9-x^2) occurs when x=0 and
this maximum is sqrt(9) = 3
The minimum value of sqrt(9-x^2) occurs when x=+-3 and
this minimum is sqrt(9-9) =0
which together give us the Range.

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