How do you graph #y= -2|x-4|#?

1 Answer
Nov 16, 2017

Answer:

For x>4
y=-2x+8

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

For x=4
y=0

Explanation:

#abs(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]}