Why is the range of this 2 variable function not inclusive of negative numbers?

[davidp92]

Homework Statement

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

 

[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.

 

[Mark44]

Welcome to PF, davidp92!

Actually the range of the function f given by f(x,y)=9-x²-y² is (∞, 9].

I think you mean (-∞, 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.