How do you write y = -2|x-4|+4 as piecewise functions?

Jul 8, 2017

 y = { 2(x-2) , x<4
 y= { -2(x-6), x>=4

Explanation:

$y = - 2 | x - 4 | + 4$ ; Putting x-4=0 ; x = 4  [Absolute part only]

Putting $x < 4$ we get $x - 4$ as negative and putting $x > 4$ we get $x - 4$ as positive.

$y = - 2 \cdot - \left(x - 4\right) + 4 , x < 4$ or
$y = - 2 \cdot \left(- x + 4\right) + 4 , x < 4$ or
$y = 2 x - 8 + 4 \mathmr{and} y = 2 x - 4 \mathmr{and} y = 2 \left(x - 2\right) , x < 4$ AND

$y = - 2 \cdot \left(x - 4\right) + 4 , x \ge 4$ or
$y = - 2 x + 8 + 4 , x \ge 4$ or
$y = - 2 x + 12 \mathmr{and} y = - 2 \left(x - 6\right) , x \ge 4$

So written in piecewise function

 y = { 2(x-2) , x<4
 y= { -2(x-6), x>=4

graph{-2|x-4|+4 [-10, 10, -5, 5]} [Ans]