How do you graph #y = 2 | x - 1 | - 3#?

1 Answer
May 17, 2017

Answer:

Substitute the definition: #|A|={(A;A>=0),(-A;A<0):}#
Simplify the domain restrictions and the equation.
Start at the common point plot and plot the two rays extending from that point.

Explanation:

Given: #y = 2 | x - 1 | - 3#

Substitute #(x-1)# for #|x-1|# and the domain restriction #x-1>=0#
#y = 2( x - 1 ) - 3; x-1>=0#

Substitute #(1-x)# for #|x-1|# and the domain restriction #x-1<0#
#y = 2( 1-x ) - 3; x-1<0#

Simplify the domain restrictions:

#y = 2( x - 1 ) - 3; x>=1#
#y = 2( 1-x ) - 3; x<1#

Simplify the equations:

#y = 2x - 5; x>=1#
#y = -2x - 1; x<1#

Please observe that the common point is #(1,-3)#; the graph is two rays extending from this point.

Another point on the line with positive slope is #(2,-1)#
Another point on the line with negative slope is #(0,-1)#

The following is a graph of the function:
graph{y=2|x-1|-3 [-14.24, 14.24, -7.12, 7.12]}