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How do you write #y = | x - 2|# into piecewise functions?

Answer 1

Isaiah Anthony

#y=2-x, x in (-oo, 2] and y=x-2, x in [2, oo)#

The graph of #y=|x-2|# is continuous.

(2, 0) is a node.

The graph for the straight line representing

the piecewise unction #y=2-x, x in (-oo, 2]# of slope - 1,

turns through a right angle at x=2,

for the next piecewise function #y=x-2, x in [2, oo)#,

with slope 1..

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Answer 2

Jameson Allen

To write ( y = | x - 2| ) into piecewise functions:

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