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Math Help - Split/Piece Wise Functions with absolute values

  1. #1
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    Split/Piece Wise Functions with absolute values

    In my calculus class, we are going over these as a review, but I have completely forgotten how to do them and the teacher didn't really explain them since he assumed we knew them.

    We are supposed to make several functions into split functions.

    Y=5-|2x-10| and Y=2x^2-|x^2-9|

    I have completely forgotten how to do these so if anybody could explain them that'd be great. I have to get these quickly.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by lawlerskates View Post
    In my calculus class, we are going over these as a review, but I have completely forgotten how to do them and the teacher didn't really explain them since he assumed we knew them.

    We are supposed to make several functions into split functions.

    Y=5-|2x-10| and Y=2x^2-|x^2-9|

    I have completely forgotten how to do these so if anybody could explain them that'd be great. I have to get these quickly.
    do you remember how we define absolute values?

    recall that |x| = \left \{ \begin{array}{lr} x & \mbox{ if } x \ge 0 \\ & \\ -x & \mbox{ if } x < 0 \end{array} \right.

    does that help?

    Hint: of course, you are not just dealing with x here, but functions. the same rule applies. you can replace x with f(x) in the above definition as well
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    Yea I remember that, but I'm really just blanking out on these ones.

    For the 5-|2x-10|, when I split them, do I make the first one 5-(2x-10) and the second 5+(2x+10)?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by lawlerskates View Post
    Yea I remember that, but I'm really just blanking out on these ones.

    For the 5-|2x-10|, when I split them, do I make the first one 5-(2x-10) and the second 5+(2x+10)?
    nope

    going strictly by the definition:

    5 - |2x - 10| = \left \{ \begin{array}{lr} 5 - (2x - 10) & \mbox{ if } 2x - 10 \ge 0 \\ & \\ 5 - [ -(2x - 10)] & \mbox{ if } 2x - 10 < 0 \end{array} \right.

    now just simplify things (including the ranges)
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  5. #5
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    Alright I'm finally starting to get it again. Thanks a lot.
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