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Math Help - Continous Functions

  1. #1
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    Exclamation Continous Functions

    hi,
    can someone please explain to me the concept of continuity?..... when they say determine the values of x for which a function is continous..what do they mean and how is it done? ..thanks
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  2. #2
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    continuous just means that the graph is connected.

    e.g. if you have a piece meal function:
    x - 1 for x> 0
    and x for x< 0

    There is discontinuity at x =0, as there are no values for x = 0.

    also, if you have a hyperbola like y = 1/x. It is discontinuous when x = 0, as there is an asymptote there.

    to find continous/discontinous points:

    continous: occurs when there is no gap in the curve. Find the values for which x cannot be equal to. e.g. \sqrt{x-2} x -2 >> 0. x must be greater or equal to 2. and hence, the curve is continuous when x is >>2.
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  3. #3
    MHF Contributor Bruno J.'s Avatar
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    Quote Originally Posted by differentiate View Post
    continuous just means that the graph is connected.
    Not exactly. You mention yourself that the hyperbola xy=1 is discontinuous at 0, but its graph is connected.
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  4. #4
    Moo
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    Quote Originally Posted by Bruno J. View Post
    Not exactly. You mention yourself that the hyperbola xy=1 is discontinuous at 0, but its graph is connected.
    What he said is : continuous => connected.
    it doesn't mean that connected => continuous

    And for this function, if you look at the graph on the whole domain, it's not connected at all... (negative vs. positive domain)
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