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Math Help - What are some reasons a function would be discontinuous?

  1. #1
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    What are some reasons a function would be discontinuous?

    I need to think of some functions that would be discontinuous at x=-4 but continuous at every other value of x and they have to be discontinuous for different reasons.
    so far i have:
    1) f(x) = 1/(x+4)
    2) f(x) = 3^(1/(x+4))
    i just need one more!
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  2. #2
    MHF Contributor undefined's Avatar
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    Quote Originally Posted by yess View Post
    I need to think of some functions that would be discontinuous at x=-4 but continuous at every other value of x and they have to be discontinuous for different reasons.
    so far i have:
    1) f(x) = 1/(x+4)
    2) f(x) = 3^(1/(x+4))
    i just need one more!
    You can easily produce a removable dicontinuity by taking a normal function like f(x)=x and multiplying it by (x+4)/(x+4).

    You can also do a piecewise function, such that the limit exists and the function is defined, but the two values are not equal.

    Still another example is the floor function.
    Last edited by undefined; September 28th 2010 at 09:30 PM. Reason: had an error
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