State whether the graph has infinite discontinuity, jump discontinuity, point discontinuity, or is continuous.?

State whether the graph f(x) = x^3 - x^2 - 12x / x + 3 has infinite discontinuity, jump discontinuity, point discontinuity, or is continuous.

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4 Answers

  • 1 decade ago
    Favorite Answer

    this a point discontinuity, at x=3 , the limit exists, but this is discontinuous function (undefined at x=3),

    keep in mind that:

    f(x)=(x-1)/(x-1) does not equal to f(x)=1 , the first is not continuous (undefined at x=1), while the latter is continuous everywhere.

  • goober
    Lv 7
    1 decade ago

    It has a discontinuity at x = -3. I don't know the precise definitions of the various types of discontinuity but infinite seems to be a good description of what happens.

  • Anonymous
    7 years ago

    The function is actually continuous/there's not enough information given in the question.

    The domain and codomain of the function have not been given. For it to be a function, it needs to be defined at every point in its domain. As the function given is not defined at x=3, the only assumption you can make is that the function has domain R/{3} (ie all real numbers except 3). If that is the case, then it is continuous at every point in its domain, so is a continuous function.

    To extend the function to the entire real line, you need to assign a value to f(3). If you assign the value -3, then it is continuous (as that is the limit as x->3), but if you assign a different value it is not, and will have a discontinuity at x=3.

  • witty
    Lv 4
    1 decade ago

    the function is discontinuous

    however, since

    (x+3)(x -4)x / x+3

    = x(x-4)

    its limit exists

    it is a point discontinuity and can be removed.

    but now it is definitely a discontinuous function

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