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Math Help - Identify the discontinuity. f'(x) for the f(x).

  1. #1
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    Identify the discontinuity. f'(x) for the f(x).

    Identify the discontinuity. f'(x) for the f(x).-capture.png

    I did graph the inequality.Identify the discontinuity. f'(x) for the f(x).-graphs.png

    Is see the y intercept at 5 and what looks like opposite slopes. I replaced a with 5. The notation of question e):

    f'(x) for the f(x) in d)

    is a little bit confusing to me. If I am correct the f'(x)=-1 and f'(x)=1 for the function in d)

    I am trying to determine how to graph:
    f'(x) for the f(x) in d)

    Thanks in advance...


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  2. #2
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    Re: Identify the discontinuity. f'(x) for the f(x).

    Part d is a v shape Just the top part of your graph. Ofcourse, you don't know what the value of 'a' is so you don't know if the vertex is above or below the x axis, but you do know it is a V
    When x>0 the gradient is +1, when x<0 the gradient is -1
    What happens when x=0? The graph is not defined. There is no f(x) value when x=0, f(x) is undefined when x=0 so f(x) is discontinuous when x=0
    You show this on a graph by putting an open circle around this point (0,a)

    Now when x>0 f'(x)=1 This is just a line horizontal to the x axis starting at (0,1) x=0 is not included so it will start with an open circle
    And, when x<0 f'(x)=-1 This is just a line horizontal to the x axis starting at (0,-1) x=0 is not included so it will start with an open circle

    So f'(x) is discontinuous at x=0 and the two halves start in very different places.

    (Sorry, I don't know what the words are for different types of discontinuity)
    Last edited by Melody2; November 5th 2013 at 03:37 AM.
    Thanks from sepoto
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