One way to identify how the given absolute value function graph is related to the graph of y=|x| is by plotting both graphs alongside each other.
We have also made note of a few points on both graphs to help us identify how the graph of y=|x| was translated.
Given Graph
Parent Graph
( -6, 2)
( -2, 2)
( 0, 4)
( 4, 4)
( 2, 6)
( 6, 6)
Every point on the graph of y=|x| has been translated left by 4 units. Notice that the y-value is the same, but the x-value in the given graph is 4 units less than that of the parent function.
You can quickly identify translations by observing differences in the x- and y-coordinates of vertices of both graphs. In this case, the parent function's vertex at (0,0) became the given function's vertex at (- 4,0) by translating left by 4 units.
