Results 1 to 5 of 5

Thread: 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 $\displaystyle \frac{1}{x}$ so if it'z like $\displaystyle 5 (\frac {1} {3(x)}) $ will the resulting graph be different than $\displaystyle \frac{1}{x}$
    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
    9
    Quote Originally Posted by ruscutie100 View Post
    will it stay the same if i add horizontal and vertical shifts 2 it..
    If you have $\displaystyle f(x) = \frac{1}{x}$, the vertical and horizontal asymptotes are obviously not changed by a dilation from either axis.

    But consider $\displaystyle g(x) = \frac{1}{x - 1} + 2$, 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 $\displaystyle f(x) = \frac{1}{x}$ 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 $\displaystyle f(x) = \frac{1}{x}$, then consider:

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

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

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

    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: Dec 30th 2009, 09:04 AM
  2. vertical and horizontal asymptotes
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Oct 20th 2009, 07:29 AM
  3. Horizontal and vertical asymptotes
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Sep 17th 2009, 07:31 PM
  4. Replies: 1
    Last Post: Sep 17th 2008, 10:08 AM
  5. Horizontal & Vertical Asymptotes
    Posted in the Algebra Forum
    Replies: 3
    Last Post: Nov 17th 2007, 07:20 PM

Search tags for this page

Search Tags


/mathhelpforum @mathhelpforum