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Math Help - location of asymptotes and points of discontinuity

  1. #1
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    Arrow location of asymptotes and points of discontinuity

    2x+5
    _______
    (x-1)(x+5)

    Determine the location of asymptotes and points of discontinuity if they exist.

    I know how to solve it with graphing but how do I find it without graphing?
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  2. #2
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    Quote Originally Posted by power2600 View Post
    2x+5
    _______
    (x-1)(x+5)

    Determine the location of asymptotes and points of discontinuity if they exist.
    I know how to solve it with graphing but how do I find it without graphing?
    Hello,

    I assume that you should examine the function:
    Code:
             2x+5
    f(x) = ----------
           (x-1)(x+5)
    1. Calculate the domain of f: d = IR \ {-5, 1} because the denominator must be unequal to zero. The equations x = -5 and x = 1 describe the vertical asymptotes

    2.
    Code:
             2x+5
    f(x) = -----------
           x + 4x - 5
    The degree ofthe numerator is smaller than the degree of the denominator therefore f has a horizontal asymptote: y = 0 (or in other words: The x-axis is a sysmptote of f)

    I've attached a diagram of the function.
    Attached Thumbnails Attached Thumbnails location of asymptotes and points of discontinuity-gebr_fkt_asympt1.gif  
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