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

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

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Answer 1 · 2017-07-08T11:44:40

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

Explanation:

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

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

$y = - 2 \cdot - (x - 4) + 4, x < 4$ $y = -2* -(x-4) +4 , x <4$ or
$y = - 2 \cdot (- x + 4) + 4, x < 4$ $y = -2* (-x+4) +4 , x <4$ or
$y = 2 x - 8 + 4 or y = 2 x - 4 or y = 2 (x - 2), x < 4$ $y= 2x -8 +4 or y=2x-4 or y = 2(x-2) , x<4$ AND

$y = - 2 \cdot (x - 4) + 4, x \geq 4$ $y = -2* (x-4) +4 , x >=4$ or
$y = - 2 x + 8 + 4, x \geq 4$ $y = -2x+8 +4 , x >=4$ or
$y = - 2 x + 12 or y = - 2 (x - 6), x \geq 4$ $y = -2x+12 or y= -2(x-6), x >=4$

So written in piecewise function

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

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

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

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

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