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

Answer 1

Genesis Allen

The piecewise function is #y={(-2x+12 if x>=4),(2x-4 if x<4):}#

The function is

#y=-2|x-4|+4#

#x-4>=0#, #=>#, #x>=4#

Therefore,

#y=-2|x-4|+4={(-2(x-4)+4 if x>=4),(-2(-(x-4))+4 if x<4):}#

#y={(-2x+12 if x>=4),(2x-4 if x<4):}#

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

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Answer 2

Avery Alexander

You can write ( y = -2|x-4|+4 ) as a piecewise function as follows:

[ y = \begin{cases} -2(x-4) + 4 & \text{if } x < 4 \ -2(-(x-4)) + 4 & \text{if } x \geq 4 \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.