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Math Help - Increasing and Decreasing function

  1. #1
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    Increasing and Decreasing function

    I have been searching the definition for increasing and decreasing functions.

    Most of the definition define f such that f : A -> R where A is a subset of real numbers R. Then f is increasing if f(y)>f(x) where y>x and x, y in A.

    Is it necessary that the domain of f must be a subset of R?

    Can the domain be R?

    Thanks for those who help...
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  2. #2
    Super Member angel.white's Avatar
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    if your y value is increasing as your x value is increasing, the function is increasing.

    for example f(x) = x

    if x = 0, y = 0
    if x = 1, y = 1

    So as you go from left to right, your y value gets higher, thus it is increasing.
    -----
    I've attached some graphs of increasing functions.

    (I feel like a kid with candy)

    edit: Note that f(x)=x^{3} is not increasing at the point (0,0), but it is increasing everywhere else.
    Attached Thumbnails Attached Thumbnails Increasing and Decreasing function-increasing-functions.png  
    Last edited by angel.white; December 4th 2007 at 02:23 AM.
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  3. #3
    Super Member angel.white's Avatar
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    And here are some examples of decreasing functions, a decreasing function has the y value get lower as x increases.

    So as x goes from left to right, the value of f(x) goes down.

    Again, note that f(x)=-(x-5)^{3} is not decreasing at the point (0,0)
    Attached Thumbnails Attached Thumbnails Increasing and Decreasing function-decreasing-functions.png  
    Last edited by angel.white; December 4th 2007 at 02:24 AM. Reason: changed -x^3 to -(x-5)^3 to "unclump" the graphs
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