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

1 Answer
Jul 8, 2017

Answer:

# y = { 2(x-2) , x<4#
# y= { -2(x-6), x>=4#

Explanation:

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

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

# y = -2* -(x-4) +4 , x <4 # or
# y = -2* (-x+4) +4 , x <4 # or
#y= 2x -8 +4 or y=2x-4 or y = 2(x-2) , x<4# AND

# y = -2* (x-4) +4 , x >=4 # or
# y = -2x+8 +4 , x >=4 # or
# y = -2x+12 or y= -2(x-6), x >=4 #

So written in piecewise function

# y = { 2(x-2) , x<4#
# y= { -2(x-6), x>=4#

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