Absolute Value Piecewise Problem

**slice38** · August 11th 2012, 05:45 AM

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

**Prove It** · August 11th 2012, 05:55 AM

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

$\displaystyle \begin{align*} f(x) &= -|x - 2| \\ &= -\begin{cases} x - 2 \textrm{ if } x - 2 \geq 0 \\ -(x - 2) \textrm{ if } x - 2 < 0 \end{cases} \\ &= -\begin{cases} x - 2 \textrm{ if } x \geq 2 \\ -x + 2 \textrm{ if } x < 2 \end{cases} \\ &= \begin{cases} -x + 2 \textrm{ if } x \geq 2 \\ x - 2 \textrm{ if } x < 2 \end{cases} \end{align*}$