How do you write #y = |x+5|# as a piecewise function?

Answer 1

Genesis Allen

#|x+5|=x+5# if #x>=-5# and

#|x+5|=-x-5# if #x<-5#

#|a|# is a split function as

#|a|=a# if #a>=0# and #|a|=-a# if #a<0#

Similarly, we can write #y=|x+5|# as

#|x+5|=x+5# if #x+5>=0# i.e. #x>=-5# and

#|x+5|=-x-5# if #x+5<0# i.e. #x<-5#

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Answer 2

Genesis Allen

The piecewise function for ( y = |x+5| ) is:

[ y = \begin{cases} -(x+5) & \text{if } x < -5 \ x+5 & \text{if } x \geq -5 \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.

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