In order to graph an inequality we work in 3 steps:
First we graph our boundaries; we dash the line if the values on
the line are not included in the boundary. If the values are
included we draw a solid line as before.
Second we test a point in each region. If one point on one side
of the line satisfies our inequality, the coordinates of all the
points on the same side of the line will satisfy the same
inequality.
Last we shade the region whose coordinates satisfy our
inequality.
Example
Graph
Our absolute value function has two conditions to consider:
As the first step we graph our boundaries, the lines will be
dashed since the values on the lines are not included in the
boundaries:
Second we should test one point, we choose to test (0,2):
Since our point satisfies our inequality, the coordinates of all
the points on the same side of the lines will satisfy the same
inequality.
As a last step we shade this region:
Videolesson: Graph f(x) < Ix-1I-7