Results 1 to 2 of 2
Like Tree1Thanks
  • 1 Post By Plato

Thread: Defining a continuous piecewise function

  1. #1
    Member
    Joined
    Mar 2017
    From
    Toronto
    Posts
    161
    Thanks
    1

    Question Defining a continuous piecewise function

    I would really appreciate someone's help on a piecewise function-related question that I have. I'm wondering in the case when a piecewise function is continuous, does it matter which sub-function (in the case when there's two sub-functions) is defined as the less than or equal to sub-function? I would think that it would not matter since they are connected after all, but I just want confirmation for my reasoning is right. I attached an example in this post. Thanks
    Defining a continuous piecewise function-17408029_1342014722521285_922736812_o.jpg
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    21,083
    Thanks
    2565
    Awards
    1

    Re: Defining a continuous piecewise function

    Is it clear to you that these two functions are equivalent?
    $f(x)=\begin{cases}\sqrt{x} &: x\ge 1 \\ |x| &: x<1\end{cases}$ and $g(x)=\begin{cases}\sqrt{x} &: x>1 \\ |x| &: x\le 1\end{cases}$

    If not surely the only question is possibly about $x=1$.
    But $\displaystyle{ f(1) = {\lim _{x \to 1}}f(x) = 1 = g(1) = {\lim _{x \to 1}}g(x) }$ removes all doubt.
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: Oct 20th 2016, 05:23 AM
  2. Replies: 3
    Last Post: Sep 12th 2012, 02:38 PM
  3. Replies: 14
    Last Post: Oct 7th 2011, 09:45 PM
  4. Laplace Transform of a Continuous Piecewise Function
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: Nov 28th 2010, 03:27 PM
  5. Piecewise continuous
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Oct 30th 2008, 12:23 PM

Search Tags


/mathhelpforum @mathhelpforum