# How do you write y=|2x-4|  as a piecewise function?

Feb 14, 2017

$y = 2 | x - 2 | \ge 0$.

$y = 2 \left(x - 2\right) , x \ge 2 \mathmr{and} y = - 2 \left(x - 2\right) , x \le 2$. See Socratic graph.

#### Explanation:

$y = 2 | x - 2 | \ge 0$.

$= 2 \left(x - 2\right) , x \ge 2 \mathmr{and}$

$- - 2 \left(x - 2\right) , x \le 2$.

Graphically, the given equation represents the V-shaped

semi pair of lines

$\left({y}^{2} - - 4 {\left(x - 2\right)}^{2}\right) = 0$. The half that is off is below the point of

intersection (2, 0).

graph{2|x-2| [-10, 10, -5, 5]}