Inequalities can be shown as regions in the Cartesian plane. You can shade regions on a number plane that involve either linear or non-linear graphs. This means that we can have regions bounded by a circle or a parabola, or any of the other graphs you have drawn in this chapter.
Regions can be bounded or unbounded.
A bounded region means that the line or curve is included in the region.
1. Find the region defined by .
First, sketch y = x + 2 as an unbroken line.
On one side of the line, y > x + 2 and on the other side, y < x + 2.
To find which side gives y > x + 2, test a point on one side of the line (not on the line).
For example, choose (-2, 1) and substitute into:
y > x + 2
1 > -2 + 2
1 > 0 (this is true)
This means that (-2, 1) lies in the region y > x + 2. The region is on the this (left or upper) side of the line.
2. Find the region defined by
3. Sketch the region .