Results 1 to 3 of 3

Math Help - prove about functions

  1. #1
    Newbie
    Joined
    Dec 2006
    Posts
    7

    prove about functions

    1) Is this statement true or false.
    A rational function can never cross one of its asymptotes?
    Justify your answer.

    2) What can be said about the sum or difference of
    a)two even functions
    b)two odd functions
    c)an even and odd function
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,713
    Thanks
    632
    Hello, kishan!

    1) Is this statement true or false?
    A rational function can never cross one of its asymptotes.
    Justify your answer.

    A function cannot cross one of its vertical asymptotes.
    . . However, it can cross its horizontal asymptote.

    Recall that a horizontal asymptote describes the behavior of the graph as x \to \pm\infty
    That is, the graph may approach a finite value at the extreme right or extreme left;
    . . but anything can happen "locally".


    Perhaps the simplest example is a Serpentine Curve: . y \:=\:\frac{x}{x^2+1}
    Code:
                              |
                              |       *
                              |   *       *
                              | *           *
                              |*                *
                              |                       * 
    - - - - - - - - - - - - - * - - - - - - - - - - - - -
      *                       |
            *                *|
                *           * |
                  *       *   |
                      *       |
                              |

    It has a horizontal asymptote: . y = 0 .(the x-axis)

    But it crosses the x-axis at the origin.

    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor red_dog's Avatar
    Joined
    Jun 2007
    From
    Medgidia, Romania
    Posts
    1,252
    Thanks
    5
    Quote Originally Posted by kishan View Post
    2) What can be said about the sum or difference of
    a)two even functions
    b)two odd functions
    c)an even and odd function
    a) The sum of two even functions is also an even function.
    Let f,g be two even functions.
    That means f(-x)=f(x),g(-x)=g(x),\forall x
    (f+g)(-x)=f(-x)+g(-x)=f(x)+g(x)=(f+g)(x)

    b) Prove in the same way that the sum of two odd functions is an odd function.

    c) The sum of an even function and an odd function can be any kind of function (even, odd, not even or not odd).
    For example, f(x)=x is odd, g(x)=x^2 is even, but f(x)+g(x)=x+x^2 is neither even or odd.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: November 21st 2011, 04:05 PM
  2. Prove that f^{-1}=g for given functions.
    Posted in the Calculus Forum
    Replies: 5
    Last Post: June 25th 2010, 10:51 AM
  3. Prove that following functions are continuous
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: May 14th 2010, 03:43 PM
  4. Prove these functions are orthogonal
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 20th 2009, 05:59 PM
  5. Can somebody prove - Hyperbolic functions
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 21st 2006, 05:53 AM

Search Tags


/mathhelpforum @mathhelpforum