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How do you write #f(x) = 1 - |x - 1|# as a piecewise function?

Answer 1

Eva Adamson

Piecewise, #f(x)=x, x in (-oo, 1] and f(x)=2-x, x in [1, oo)#.

#|x-1|=1-x, x in (-oo, 1] and

#=x-1, x in [1, oo)#.

So,

#f(x)=x-(1-x)=x, x in (-oo, 1]#

#=1-(x-1)=2-x, x in [1, oo)#.

Note that f(x) is continuous everywhere.

The graph is collar (inverted V)-like, with vertex at (1, 1).

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Answer 2

Kennedy Adams

You can write the function ( f(x) = 1 - |x - 1| ) as a piecewise function as follows:

[ f(x) = \begin{cases} 1 - (x - 1) & \text{if } x < 1 \ 1 - (1 - x) & \text{if } x \geq 1 \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.