# How do you write y=|6+2x|+1  as a piecewise function?

Aug 9, 2017

Piecewise function:
 y = { - 2x -5 ; x < -3
 y= { 2x +7 ; x >= -3

#### Explanation:

$y = | 6 + 2 x | + 1$

$6 + 2 x = 0$ .The absolute part is taken for zero only

$2 x = - 6 \therefore x = - 3$. Solving for $x$ , critical point is $- 3$

When  x < -3 ; 6+2x < 0 ; |6+2x| = -(6+2x)

When  x >= -3 ; 6+2x >= 0 ; |6+2x| = 6+2x

Piecewise function may be written as

 y = { -6-2x +1 ; x < -3
 y= { 6+2x +1 ; x >= -3
OR
 y = { - 2x -5 ; x < -3
 y= { 2x +7 ; x >= -3  {Ans]