Results 1 to 3 of 3

Math Help - Continuity Question with Piecewise Defined Function and Absolute Values

  1. #1
    Member
    Joined
    Jan 2011
    Posts
    156

    Continuity Question with Piecewise Defined Function and Absolute Values

    Determine the values of b and c so that the following function is continuous:

    f(x) = \left\{\begin{array}{cc}x+1,&\mbox{ if }<br />
 1< {x}< 3\\x^2 + bx + c, & \mbox{ if } \lvert x+2 \rvert \geq 1\end{array}\right

    Restating this function to remove the absolute values, I get:

    f(x) = \left\{\begin{array}{cc}x^2 + bx + c,&\mbox{ if }<br />
  {x}\leq -3\\ x^2 + bx + c, & \mbox{ if } x \geq -1\\x + 1 , &\mbox{ if } 1 < x < 3  \end{array}\right

    But this makes absolutely no sense to me since I can see no way that this function can be continuous defined like I have done it. I must be screwing up the absolute value inequality.

    Can somebody help?

    Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,804
    Thanks
    1576
    Are you sure that it's not \displaystyle x^2 + bx + c if \displaystyle |x - 2| \geq 1?

    Because then \displaystyle x - 2 \leq -1 or \displaystyle x - 2 \geq 1

    \displaystyle x \leq 1 or \displaystyle x \geq 3.

    This would at least ensure that your function is at least DEFINED for all values over your given domain...
    Last edited by Prove It; February 5th 2011 at 11:56 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jan 2011
    Posts
    156
    It says x + 2, but that has to be a typo. I'm going to treat it as x - 2, since it's the only way that I know how to solve this problem.

    Thanks.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Piecewise defined function
    Posted in the Algebra Forum
    Replies: 8
    Last Post: April 20th 2009, 03:25 PM
  2. Piecewise Defined Function
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: December 29th 2008, 10:30 PM
  3. Absolute Values and piecewise functions
    Posted in the Algebra Forum
    Replies: 8
    Last Post: August 26th 2008, 05:43 PM
  4. piecewise defined function help!
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 30th 2007, 09:18 PM
  5. Piecewise-Defined Function
    Posted in the Pre-Calculus Forum
    Replies: 6
    Last Post: January 20th 2007, 07:05 AM

Search Tags


/mathhelpforum @mathhelpforum