# How do you write g(x) = -2|x+1| as a piecewise function?

Mar 13, 2016

$g \left(x\right) = \left\{\begin{matrix}- 2 \left(x + 1\right) & x \ge - 1 \\ 2 \left(x + 1\right) & x < - 1\end{matrix}\right.$

#### Explanation:

$\left\mid t \right\mid = \left\{\begin{matrix}t & t \ge 0 \\ - t & t < 0\end{matrix}\right.$

Hence:

$\left\mid x + 1 \right\mid = \left\{\begin{matrix}\left(x + 1\right) & x \ge - 1 \\ - \left(x + 1\right) & x < - 1\end{matrix}\right.$

Multiply by $- 2$ to get:

$g \left(x\right) = \left\{\begin{matrix}- 2 \left(x + 1\right) & x \ge - 1 \\ 2 \left(x + 1\right) & x < - 1\end{matrix}\right.$