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Asymptotes curve (1-2x)/(3x+5)

  1. Jun 15, 2003 #1
    I the curve (1-2x)/(3x+5). I have been asked to find the verticle and horizontal asymptotes. Can anyone help me with a strategy?
    Last edited by a moderator: Feb 5, 2013
  2. jcsd
  3. Jun 15, 2003 #2
    Here are some hints.

    Vertical asymptote: check the demominator, see which point doesn't exist.

    horizontal asymptote: take limit of f(x) as x tends to infinity. What is the relation between the limit value you find and the horizontal asymptote?
    Last edited: Jun 15, 2003
  4. Jun 15, 2003 #3


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    I dunno but that answer looks a little too complicated...

    y = (1-2x)/(3x+5)
    3xy + 5y = 1 - 2x
    x = (1 - 5y )/(3y + 2)

    Now, find the value y can't have....

    but beware, I have been wrong before (intentionally of course! )
  5. Jun 15, 2003 #4
    That's interesting. I never thought of it like that. That suggests to me that the horizontal asymptote of a function should be equivalent to the vertical asymptote of its inverse (if the inverse exists). Let's see. That might be too general.

    Say y(x)= (Ax^n+B)/(Cx^n+D)
    Then y=A/C is its horizontal asymptote.
    It's inverse:
    Has as its vertical asymptote y=A/C
    (For the second graph, x is a function of y - so y=A/C is a vertical line).

    Of course, the converse should also be true.
    I like that. It shows how arbitrary our placement of the axes and the definition of our variables are.
    My algebra skills break down from there. I tried having nonzero coefficients for other powers of x [eg. x^(n-1)] but I'm not sure I can solve for x in that case.
  6. Jun 25, 2003 #5
    In this case the largest degrees of the variables are the same (to the first). So for horizontal asymtotes dont u just take the ratio:

    -2x + 1
    3x + 5

    So the horizontal asymtote is (-2/3)

  7. Jun 25, 2003 #6
    To find horizontal asymptotes (when dealing with rational functions of polynomials), divide both top and bottom of the fraction by the highest power of x and take the limit as x->[oo]
    Essentially, all terms which have an x that is less than the highest power will tend to zero, and that is a shortcut that most people use.

    For example, if the highest power of x is in the denominator, all the terms in the numerator will tend to zero and that asymptote is y=0.

    btw, an asymptote is a line (or some y-value) that the graph approaches, so it should be written as y=k, rather than just k, although I'm sure anyone would know what you mean if you said the horizontal asymptote is -2/3
    Last edited: Jun 25, 2003
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