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.

### Examples

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

### Show Answer

The equation is a circle, radius 1 and centre (0, 0).

Draw as a broken line, since the region does not include the curve.

Choose a point inside the circle, say (0, 0)

(This is false)

So the region lies outside the circle.

3. Sketch the region .

### Show Answer