Results 1 to 5 of 5

Math Help - Are asymptotes effected by vertical/horizontal expansion or compression??

  1. #1
    Newbie
    Joined
    Sep 2007
    Posts
    18

    Are asymptotes effected by vertical/horizontal expansion or compression??

    as the question says, are the graphs effected.... the basic equation is  \frac{1}{x} so if it'z like  5   (\frac {1} {3(x)}) will the resulting graph be different than  \frac{1}{x}
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Jan 2008
    Posts
    7

    not affected

    The asymotopes wnt be affected, in that example by compression and expansion as the asymotopes lie on the x and y axis, the general steepness of the graph will increase tho.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2007
    Posts
    18

    Question

    Quote Originally Posted by chris_uk View Post
    The asymotopes wnt be affected, in that example by compression and expansion as the asymotopes lie on the x and y axis, the general steepness of the graph will increase tho.
    will it stay the same if i add horizontal and vertical shifts 2 it..
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Jan 2008
    Posts
    7
    If you added a shift to it the expansion or compression would affect the asymotopes just as it would any other point
    e.g.
    if you had y=1/x +2 where the asymotopes are at y=2 and x=0

    a vertical expansion of scale factor 2... y=2(1/x +2) can be written as y=2/x +4. Where the asymotopes are y=4 and x=0
    note: y=1/x +1 is not equal to y=1/(x+1) it wasn't very clear wen i wrote it.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by ruscutie100 View Post
    will it stay the same if i add horizontal and vertical shifts 2 it..
    If you have f(x) = \frac{1}{x}, the vertical and horizontal asymptotes are obviously not changed by a dilation from either axis.

    But consider g(x) = \frac{1}{x - 1} + 2, say. This can be got by applying appropriate translations to f(x). g(x) has a vertical asymptote x = 1 and a horizontal asymptote y = 2. (So applying translations to f(x) = \frac{1}{x} will change its asymptotes, if that's what you were asking).

    But if you want to know whether dilations will have an affect on asymptotes after translations have been added to f(x) = \frac{1}{x}, then consider:

    Dilation by factor a from horizontal axis: g(x) \rightarrow a g(x). Clearly g(x) \rightarrow h(x) = a g(x) = a \left( \frac{1}{x - 1} + 2 \right) = \frac{a}{x - 1} + 2a.

    h(x) still has a vertical asymptote x = 1 but the horizontal asymptote is y = 2a.

    Dilation by factor 1/a from vertical axis: g(x) \rightarrow g(ax). Clearly g(x) \rightarrow k(x) = g(ax) = \frac{1}{ax - 1} + 2.

    k(x) now has a vertical asymptote x = 1/a and the horizontal asymptote is still y = 2.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Vertical and horizontal Asymptotes.
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 30th 2009, 10:04 AM
  2. vertical and horizontal asymptotes
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 20th 2009, 08:29 AM
  3. Horizontal and vertical asymptotes
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 17th 2009, 08:31 PM
  4. Replies: 1
    Last Post: September 17th 2008, 11:08 AM
  5. Horizontal & Vertical Asymptotes
    Posted in the Algebra Forum
    Replies: 3
    Last Post: November 17th 2007, 08:20 PM

Search Tags


/mathhelpforum @mathhelpforum