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Piece-wise Function

  1. Aug 31, 2005 #1
    I'm doing a review of fuctions, and a nagging question popped up in my mind after completing this problem.

    After graphing y = |x| + x, express this equation as a piece-wise function with no absolute values.

    I did graph it; it was simple (following is a sketch without values):

    Now the final answer included } y = 0, where x<and=0, and y = 2x, where x>0. I found the equations by looking/calculating the slope for each separate piece. However, what I do not understand is why is it x>0 INSTEAD of x>AND=0 for y = 2x. This is perhaps trivial and easy, but I don't comprehend the reason.

    Thanks for your patience.
  2. jcsd
  3. Aug 31, 2005 #2


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    Homework Helper

    Since y = 0 for x = 0, it seems to me that you could include 0 in either of the two functions.
  4. Sep 1, 2005 #3


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    Staff Emeritus
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    It doesn't matter which side you put x=0 into since the function is continuous at 0.
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