Range of 2 variable function

1. Aug 25, 2011

davidp92

1. The problem statement, all variables and given/known data
In this example, the range is stated to be z=[0,3].
It shows 9-x^2-y^2<=9 which implies sqrt(9-x^2-y^2)<=3
But why don't we consider -3 as well?

Thanks

2. Aug 25, 2011

I like Serena

Welcome to PF, davidp92!

Actually the range of the function f given by f(x,y)=9-x2-y2 is (∞, 9].
So I have to assume that you're talking about a different function.

Presumably you intended f(x,y)=√(9-x2-y2) which indeed has a range of [0,3].
Note that the square root function is defined as a function that always results in a non-negative number.

3. Aug 25, 2011

Staff: Mentor

I think you mean (-∞, 9].