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Range of 2 variable function

  1. Aug 25, 2011 #1
    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?

  2. jcsd
  3. Aug 25, 2011 #2

    I like Serena

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    Homework Helper

    Welcome to PF, davidp92! :smile:

    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.
  4. Aug 25, 2011 #3


    Staff: Mentor

    I think you mean (-∞, 9].

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