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
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 \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*} $