How do you translate "The absolute value of the difference y and 2" into an algebraic expression?

Answer 1

From the definition of an absolute value,
#|y-2| = #
(a) #= y-2# for any #y-2>=0# (that is, #y >= 2#) OR
(b) #= -(y-2) = 2-y# for any #y-2<0# (that is, #y < 2#)

The preceding response adheres to the definition of absolute value:

#|X| =# (by definition) (a) #= X# for non-negative #X# (that is, #X >= 0#)values OR (b) #= -X# for negative #X# (that is, #X < 0#)values.

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Answer 2

Eva Adamson

[|y - 2|]

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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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