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Math Help - Points of Discontinuity

  1. #1
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    Points of Discontinuity

    Here is the graph: http://i.imgur.com/5a7wi.png

    There is a removable discontinuity at x=-3 -- that is False because there is an open hole?
    There is a removable discontinuity at x=-1 - is that false because there is an open hole and one closed?
    There is a removable discontinuity at x=1 - Also false because one open and closed

    Thank You for checking
    Last edited by ritacame; September 1st 2011 at 05:19 PM.
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  2. #2
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    Re: Points of Discontinuity



    There is a removable discontinuity at x=-3 -- that is False because there is an open hole? the function is continuous at x = -3

    There is a removable discontinuity at x=-1 - is that false because there is an open hole and one closed? there is an essential discontinuity at x = -1

    There is a removable discontinuity at x=1 - Also false because one open and closed the discontinuity at x = 1 is removable ... redefining the function to be f(1) = 1 "removes" it

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    Re: Points of Discontinuity

    Essential Discontinuities are not removable, correct?

    And the discontinuity at x=3 is infinite right?
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    Re: Points of Discontinuity

    Quote Originally Posted by ritacame View Post
    Essential Discontinuities are not removable, correct? correct

    And the discontinuity at x=3 is infinite right? yes
    ...
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  5. #5
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    Re: Points of Discontinuity

    There is a choice that looks like this:

    What does that mean? Is it meaning that at negative infinity it DNE? Thats True because its an infinite discontinuity right?

    Thanks
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    Re: Points of Discontinuity

    the notation is stating the behavior of the function as x approaches 3 ... f(x) goes to -infinity, therefore the limit does not exist.
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