Results 1 to 2 of 2

Math Help - Solving Rational Equation's Oblique(slant) Asymptote

  1. #1
    Senior Member
    Joined
    Nov 2008
    Posts
    425

    Solving Rational Equation's Oblique(slant) Asymptote

    I have a quick question, the oblique asymptote of this rational equation is as follows:

    f(x)=(x^2-2x-5)/(x-1)

    oblique asymptote: y=x-1

    But my question is, would you write the answer as
    y=x-1
    or would you write it like you are answering for a horizontal asymptote ie.
    as x -> +-infinity, y -> 1

    and one more question, is it true that a function CAN cross the horizontal asymptote but cannot cross the vertical one?

    thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1

    Asymptotes

    Hello skeske1234
    Quote Originally Posted by skeske1234 View Post
    I have a quick question, the oblique asymptote of this rational equation is as follows:

    f(x)=(x^2-2x-5)/(x-1)

    oblique asymptote: y=x-1

    But my question is, would you write the answer as
    y=x-1
    or would you write it like you are answering for a horizontal asymptote ie.
    as x -> +-infinity, y -> 1

    and one more question, is it true that a function CAN cross the horizontal asymptote but cannot cross the vertical one?

    thanks
    I think both ways make sense: it just depends what the question is. If it is 'What is the equation of the asymptote?' then the answer is y=x-1. (Or, in the case of the horizontal asymptote you mention: y=1).

    But if the question is: 'Describe the behaviour of the function as x \rightarrow\infty' then you could say things like 'As x \rightarrow \infty, y \rightarrow x-1'

    As to your second question, since a function has at most only one value for each value of x, a function cannot cross any vertical line, whether it's an asymptote or not.

    Grandad
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Oblique asymptote
    Posted in the Algebra Forum
    Replies: 3
    Last Post: March 2nd 2011, 03:41 AM
  2. Slant or oblique asymptote
    Posted in the Algebra Forum
    Replies: 1
    Last Post: March 19th 2010, 05:47 AM
  3. Replies: 7
    Last Post: March 16th 2010, 09:22 PM
  4. Slant/Oblique Asymptote
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 11th 2009, 02:40 PM
  5. How do I write an equation with a slant asymptote?
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: March 23rd 2009, 01:35 PM

Search Tags


/mathhelpforum @mathhelpforum