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Asymptotes and functions

  1. Sep 28, 2009 #1
    1. The problem statement, all variables and given/known data
    Make an example of a possible equation whose graph got the asymptotes:
    a)
    x=3 and y=5
    b)
    x=-2 and y=3


    2. Relevant equations



    3. The attempt at a solution
    I have no idea but I'm ready to hear those kind of solutions you might suggest me
     
  2. jcsd
  3. Sep 28, 2009 #2
    you know the asymptote of y = 1/x ? Try moving that graph around
     
  4. Sep 29, 2009 #3
    I've found out a possible solution if we state that x=3 and y=5, then we can say that
    x-a=0
    x-3=0
    x=3
    then we can put our value in and put it under our fraction so we now got:

    ( )/3-x

    Nothing in the parantese:
    Now we need the y asymptote:

    y=5
    f(0)=5 to make this statement true:
    We need to say that:
    (5x/x)/(3/x - x/x)
    x-> eternity
    so 3/x will be close to zero and in math = 0
    so we got 5/1 = 5 this equals true. So our possible equation for our asymptotes:

    5x/(3-x).

    Is there some errors in my solving this equation or is this a possible answer?
     
  5. Sep 29, 2009 #4
    Edit: Had a wrong function with the wrong sign; mrkuo is correct.

    Another one which came to mind first was 1/(x-3) + 5. This is just a shifting of the graph of 1/x.
     
    Last edited: Sep 29, 2009
  6. Sep 29, 2009 #5
    Unfortunately,

    y=5x/(3-x)

    will not produce the asymptotes x=3 and y=5, rather, x=3 and y= negative 5.

    Use y = 5x/(x-3) instead. Previous poster's answer works just as well.
     
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