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
( -5, 1)
( -5, 5)
( -3, -1)
( -3, 3)
( 3, -1)
( 3, 3)
Every point on the graph of y=|x| has been translated down by 4 units. Notice that the x-values are the same, but the y-values in the given graph are 4 units less than those of the parent function.
You can quickly identify translations by observing the 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 (0,- 4) by translating down by 4 units.
