Results 1 to 3 of 3
Like Tree1Thanks
  • 1 Post By skeeter

Math Help - f(x) = x^-n : Different values of n and their effect on the shape of the graph

  1. #1
    Newbie
    Joined
    May 2012
    From
    Australia
    Posts
    1

    f(x) = x^-n : Different values of n and their effect on the shape of the graph

    Hi, I've been working on this investigation but I do not think I have done the first task very well. The attached image shows the task outline, and the next attached image is a screenshot of 4 different graphs on one which I made to assist in explaining my problem:
    f(x) = x^-n  :  Different values of n and their effect on the shape of the graph-photo-16-05-12-7-15-37-pm.jpgf(x) = x^-n  :  Different values of n and their effect on the shape of the graph-screenshot-2012-05-16-19-53-43.png
    I graphed various the function with differing values of n, but I do not really know how to explain what the changes are...

    So far I have written the following, but I don't know if it's all relevant and if I can include more...:

    For all values of n, the graph line intersects at (1,1).
    For 0<n<1, all graphs have asymptotes at x = 0 and y = 0.
    As n --> 0, between 0<x<1, the slope becomes more negative and therefore the graph line becomes closer to the y axis near to the origin. Also, as n --> 0, when x > 1, the slope decreases, and therefore becomes closer to the x axis near to the origin.
    For n>1, as n increases, the graph lines start moving more towards the y axis near to the origin, and become closer to the x axis near the origin.

    If graphs of the function with n = 0.01, 0.1, 1, and 10 are graphed together, obvious conclusions can be drawn.
    If 0<n<1, the slope of the function for all x is small, and slowly moves towards its horizontal asymptote of y = 0.
    If n>1, the slope of the function for x is relatively large, and particularly for 0<x<1, the slope is large (i.e. more negative).


    What can I do to improve my answer by changing it/adding to it/removing from it? Thanks
    Last edited by banana123; May 16th 2012 at 02:45 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426

    Re: f(x) = x^-n : Different values of n and their effect on the shape of the graph

    note the symmetry w/r to the line y = x in quad I for the functions y = x^{-n} and y = x^{-1/n}

    what does that say about two such functions?
    Attached Thumbnails Attached Thumbnails f(x) = x^-n  :  Different values of n and their effect on the shape of the graph-symmetry.jpg  
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2013
    From
    Australia
    Posts
    1

    Re: f(x) = x^-n : Different values of n and their effect on the shape of the graph

    Hi there, I came across this forum seeing as it is relevant to the type of maths i'm doing in class right now. As written above, you talk about the line of symmetry passing through the point of intersection of (1,1) with the function y=x for all functions of y=x^(-n). Could you give me a hint to point me in the right direction as to the relationship between the two functions?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: August 16th 2011, 05:01 AM
  2. Shape of graph of quadratic functions
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 8th 2009, 05:04 AM
  3. Can't see x- and y-values on graph
    Posted in the Calculators Forum
    Replies: 2
    Last Post: March 18th 2009, 02:01 PM
  4. Replies: 5
    Last Post: March 3rd 2009, 09:33 AM
  5. Derivative and Graph shape questions
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 28th 2008, 02:23 AM

Search Tags


/mathhelpforum @mathhelpforum