How do you graph y= -2|x-4|y=−2|x−4|?

1 Answer
Tamir E.
Nov 16, 2017

For x>4
y=-2x+8

For x<4
y=(2x-8)

For x=4
y=0

Explanation:

abs(x-4)>=0|x−4|≥0
=>⇒
if x=4 => abs(x-4)=0
if x!=4 => abs(x-4)>0
=>
(-2)*(abs(x-4))<=0
=>
if x=4 => -2abs(x-4)=0
if x!=4 => -2abs(x-4)<0

So we will separate to 3 cases:
case 1: x>4
case 2: x=4 => y=0
case 3 x<4

case 1 (x>4):
=> y=(-2)*(x-4)
=> y=-2x+8
=> m=-2 , y_(0)=8

case 3 (x<4):
=> y=(-2)*(-1)(x-4)
=> y=(-2)(-x+4)
=> y=(2x-8)
=> m=2 , y_(0)=-8

graph:
graph{-2abs(x-4) [-10, 10, -5, 5]}

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