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How to know if this irrational function has no asymptotes?

  1. Sep 18, 2015 #1
    1. The problem statement, all variables and given/known dat
    F(x)=x+1-3sqrt((x-1)/(ax+1))
    For which value of a ,(c) has no asymptote?
    2. Relevant equations


    3. The attempt at a solution
    I know if a>0 then (c) will have 2 asymptote
    And if a<o then (c) will have 1 vertical asymptote.
    But I can't find any value of a so that (c) has no asymptote. Please give me some hints thank you.

     
  2. jcsd
  3. Sep 18, 2015 #2

    RUber

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    What is leftover after you have eliminated a>0 and a<0? There is only one value possible.
     
  4. Sep 18, 2015 #3
    a=0? But still it has an O.A.
     
  5. Sep 18, 2015 #4

    RUber

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    I don't see what you are saying? Your denominator would be (0x+1) = 1.
     
  6. Sep 18, 2015 #5

    RUber

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    I see now...you meant Oblique Asymptote.
    I don't think this would have one.
    By scale, yes -- the trend is in the direction of y = x as x gets large, but you can't argue that the function value gets closer to the line in the limit.
     
  7. Sep 18, 2015 #6

    Mark44

    Staff: Mentor

    If a = 1, the part inside the radical approaches 1 for large values of |x|. That will give you an oblique asymptote.
    The OP hasn't been very clear, but I think the asymptotes he's referring to are one that's oblique and one that's vertical.
     
  8. Sep 18, 2015 #7
    Then it will have only an asymptotic direction (parabolic branch). Thank you.
     
  9. Sep 18, 2015 #8

    SammyS

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    Determine the domain of this function. That, of course, depends upon the value of a .
     
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