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

Answer 1

Eva Adamson

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]

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Answer 2

Kennedy Adams

The piecewise function representation of ( y = |6 + 2x| + 1 ) is:

[ y = \begin{cases} 6 + 2x + 1 & \text{if } 6 + 2x \geq 0 \ -(6 + 2x) + 1 & \text{if } 6 + 2x < 0 \ \end{cases} ]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.