# How do you write y = | x - 2| into piecewise functions?

Jul 2, 2016

$y = 2 - x , x \in \left(- \infty , 2\right] \mathmr{and} y = x - 2 , x \in \left[2 , \infty\right)$

#### Explanation:

The graph of $y = | x - 2 |$ is continuous.

(2, 0) is a node.

The graph for the straight line representing

the piecewise unction $y = 2 - x , x \in \left(- \infty , 2\right]$ of slope - 1,

turns through a right angle at x=2,

for the next piecewise function $y = x - 2 , x \in \left[2 , \infty\right)$,

with slope 1..