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

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Answer 1 · 2017-08-22T15:17:34

Use the definition:

#|A| = {(A; A >=0),(-A; A < 0):}#

and then simplify as needed.

Given: #y= abs(x-1)#

Use the definition where #A = x-1#:

#y = {(x-1; x-1 >=0),(-(x-1); x-1 < 0):}#

Simplify the domain restrictions:

#y = {(x-1; x >=1),(-(x-1); x < 1):}#

Distribute the minus sign:

#y = {(x-1; x >=1),(1-x; x < 1):} larr# the answer.