Graphing Absolute Value Inequalities

Graphing Absolute Value Inequalities

How to graph absolute value inequalities: examples and their solutions.

Example 1

Graph the given inequaliy. y > |x| - 2

Draw y = |x| - 2 using dashed lines.
(The inequality sign doesn't include '='.)

Graphing absolute value functions

y is greater than the right side.
So color the upper region of the dashed graph.

Example 2

Graph the given inequality. |y| <= -|x| + 4

Draw |y| = -|x| + 4 using solid lines.
(The inequality sign does include '='.)

Graphing absolute value functions

y is lesser than the right side.
So color the region that includes
the lower region of the quadrant I graph.

There's another way to color the inequality.

Find a point that makes the inequality true: (0, 0).
|0| ≤ -|0| + 4 is true.
Then color the region that includes the point: (0, 0).