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Asymptote = hyperbola?

  1. Aug 26, 2011 #1
    1. The problem statement, all variables and given/known data
    If a graph has an asymptote, does that mean it's always going to be a hyperbola?


    2. Relevant equations



    3. The attempt at a solution
    Well, I started to think of y=tan(x) and y=cot(x). I believe they would be called trigonometric circular functions as they repeat, but are they still considered hyperbolas because they have asymptotes?
     
  2. jcsd
  3. Aug 26, 2011 #2
    Do you even know what a hyperbola is...?
     
  4. Aug 26, 2011 #3
    To be honest, my understanding of them is not that strong. You caught me. This is why I am asking.
     
  5. Aug 26, 2011 #4
    Do you have a book?
     
  6. Aug 26, 2011 #5

    Mark44

    Staff: Mentor

    The graph of y = ln(x) has a vertical asymptote, but does not represent a hyperbola.
     
  7. Aug 26, 2011 #6
    Yep, I have calculus books. Unfortunately, they don't go into hyperbola's hardly at all. The one I have for school just deals with parabolas.
     
    Last edited: Aug 26, 2011
  8. Aug 26, 2011 #7
    Hey, thank you. That's just what I needed :smile:
     
  9. Aug 26, 2011 #8

    SteamKing

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    Well you have access to much more than a single textbook. You can use your computer and google 'hyperbola' or 'conic section'.
     
  10. Aug 26, 2011 #9

    Mentallic

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    What about reciprocal functions of the form [tex]\frac{1}{x}[/tex] that have asymptotes at y=0,
    or rational functions with a constant non-zero asymptote such as [tex]\frac{2x}{x+1}[/tex] or even an asymptote that is a not a line, [tex]\frac{x^3-1}{x}\approx\frac{(x-1)(x^2+x+1)}{x-1}=x^2+x+1, x\neq 1[/tex]. For this function as x gets very large positive or negative, the graph approaches the parabola [itex]y=x^2+x+1[/itex]
     
  11. Aug 26, 2011 #10

    Mark44

    Staff: Mentor

    This is a hyperbola. The central axis is rotated by 45°.

    This is the same as 2 + (-2)/(x + 1), so this is just the translation and stretching of y = 1/x, so is also a hyperbola.
     
  12. Aug 27, 2011 #11

    Mentallic

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    Oh yes of course, why did my mind instantly jump to the general form of a hyperbola...?

    Yes I'm aware of the second example's translations, but I don't really see why I bothered mentioning it now that you brought it up.

    Clearly my brain's still in holiday mode :zzz:
     
  13. Aug 27, 2011 #12

    Mark44

    Staff: Mentor

    Happens to us all...
     
  14. Aug 27, 2011 #13
    Same here, man. Same here. Just started senior year.

    True, I have been doing research on the internet. Every time I get on a site, it just wants to talk about those hyperbola's symmetric along the x or y axis. I have a decent understanding of them, just not these like 1/x lol.
     
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