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Math Help - Absolute Value Piecewise Problem

  1. #1
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    Absolute Value Piecewise Problem

    I'm hoping that someone can help me understand why I'm getting this wrong. I think I understand the rules, but maybe not.

    Thanks,
    Mike

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  2. #2
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    Re: Absolute Value Piecewise Problem

    Moving 2 units to the right: x -> x - 2, giving |x| -> |x - 2|

    Reflecting in the x axis: f(x) -> -f(x), giving |x - 2| -> -|x - 2|.

    So your function is

    \displaystyle \begin{align*} f(x) &= -|x - 2| \\ &= -\begin{cases} x - 2 \textrm{ if } x - 2 \geq 0 \\ -(x - 2) \textrm{ if } x - 2 < 0 \end{cases} \\ &= -\begin{cases} x - 2 \textrm{ if } x \geq 2 \\ -x + 2 \textrm{ if } x < 2 \end{cases} \\ &= \begin{cases} -x + 2 \textrm{ if } x \geq 2 \\ x - 2 \textrm{ if } x < 2 \end{cases} \end{align*}
    Thanks from slice38
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    Re: Absolute Value Piecewise Problem

    Quote Originally Posted by slice38 View Post
    I'm hoping that someone can help me understand why I'm getting this wrong. I think I understand the rules, but maybe not.
    You almost have it.
    f(x) = \left\{ {\begin{array}{*{20}{c}}{ - x + 2,}&{x \ge 2}\\{x - 2,}&{x < 2}\end{array}} \right.
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