How do you write #y=3abs(x-1)+2# as a piecewise function?

1 Answer
Shantelle
Oct 8, 2017

y = {#3x-1, x>=1#
{#-3x+5, x<1#

Explanation:

First, solve for #x - 1 >= 0# (an absolute value equation must be a positive number)
So #x >= 1#

Now, you separate it into 2 different equations:
#y = {3(x-1)+2, x >=1#
#{-3(x-1)+2, x<1# this one has to be the opposite of the first system, so you insert a negative to the first part and change the #>=# to #<#
(both the equations are supposed to be in one "{" but I can't type that out properly)

So now you just simplify the equations:
The 1st one becomes:
#3x-3+2, x>=1# then
#3x-1, x>=1#

The 2nd one becomes:
#-3x+3+2, x<1# then
#-3x+5, x<1#

So the final answer as a piecewise function is:
y = {#3x-1, x>=1#
{#-3x+5, x<1#

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