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Sketch graphs showing vertical & horizontal asymptotes and relative extrema

  1. Jun 16, 2011 #1
    1. The problem statement, all variables and given/known data
    Sketch the graphs of the following function showing vertical and horizontal asymptotes and relative extrema:

    f(x) = (x2-1)/(x2-4)


    2. Relevant equations
    Limits, zeroes, derivatives


    3. The attempt at a solution
    I know that I have the majority of the answers right, the only problem I'm having is with part of the vertical asymptote.

    VA = positive and negative 2

    The problem is with -2:

    lim (-22-1)/(-2+)2-4)
    x->-2+

    = (4-1)/(4+-4) = +infinity

    lim ((-2)2-1)/((-2-)2-4)
    x->-2-

    = (4-1)/(4--4) = negative infinity

    But my graphing calculator shows the exact opposite ):!

    Any help is appreciated! Thank you <3
     
  2. jcsd
  3. Jun 16, 2011 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    The limit as x->(-2)+ is +infinity. The limit as x->(-2)- is -infinity. I'm not sure what your graphing calculator's problem is.
     
  4. Jun 16, 2011 #3
    ...I guess I'm sketching the graph wrong then....Thank you for your help (:!!
     
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