# How do you write g(x) = |2 + x| - 1 into piecewise functions?

Jul 23, 2016

$g = x + 1 , x \le - 2 \mathmr{and} g = - x - 3 , x \le - 2$.
These represent the right-angled pair of straight lines through (-2. -1) that is bisected by x = -2.

#### Explanation:

$g \left(x\right) + | h \left(x\right) + c$ is the combined equation for the pair

$g \left(x\right) = h \left(x\right) , h \left(x\right) \ge 0$ and

$g \left(x\right) = - h \left(x\right) , h \left(x\right) \le 0$

Accordingly, here,

$g = x + 1 , x \le - 2 \mathmr{and} g = - x - 3 , x \le - 2$.

These represent the right-angled pair of straight lines through

$\left(x , g\right) = \left(- 2. - 1\right)$ that is bisected by $x = - 2$..