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

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Answer 1 · 2017-08-09T11:02:51

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

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

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

$2x= -6 :. x = - 3$ . 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]

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