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

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Answer 1 · 2017-08-09T11:02:51

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

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

# 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]