# How do you write  f(x) = 4 |x-3| as piecewise functions?

Jun 13, 2017

$f \left(x\right) = \left\{\left(4 x - 12 \textcolor{w h i t e}{\text{xxx") if x>= 3),(12-4xcolor(white)("xxx}} \mathmr{if} x < 3\right)\right.$
If $x \ge 3$ then $\left\mid x - 3 \right\mid = x - 3$
$\textcolor{w h i t e}{\text{XXX}} \Rightarrow 4 \left\mid x - 3 \right\mid = 4 \left(x - 3\right) = 4 x - 12$
If $x < 3$ then $\left\mid x - 3 \right\mid = - \left(x - 3\right) = 3 - x$
$\textcolor{w h i t e}{\text{XXX}} \Rightarrow 4 \left\mid x - 3 \right\mid = 4 \left(3 - x\right) = 12 - 4 x$