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How do you write write #f(x)=|x-4|# as a piecewise function?

Answer 1

#f(x)=x-4, x>=4 and f(x)=-(x-4), x<=4#, representing radial lines from [4, 0], with slopes #+-1#. It is implicit that # f(x)>=0#... .

#f(x)=|x-4|# is the combined equation for the half-line equations #f(x) = x-4, x>=4 and f(x)=4-x, x<=4#. Note that #f(x)>=0#..

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Answer 2

Elijah Allen

The piecewise function representation of ( f(x) = |x - 4| ) is as follows:

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