Inequalities and regions
Vertical regions
Graphs can be used to represent inequalities by regions (region is the area where all points obey a given rule).
For example, the region for x > 2 is represented by:
In the graph, the area where the graph is x > 2 is shown above. In this area, all of the points would be more than 2.
The line which intersects where x = 2 is drawn with a dotted line.
In the right region of the line x = 2, every point represents x > 2.
In the left region of the line x = 2, every point represents x < 2.
Horizontal regions
The rules for horizontal regions will follow the rules for the vertical regions. Therefore the graph which represents y ≤ 3 is:
In the graph, the area where the graph is y ≤ 3 is shown above. In this area, all of the points would be more than or equal to 3.
The line which intersects where y = 3 is drawn with a solid line.
In the top region of the line y = 3, every point represents y > 3 and y = 3
In the left region of the line y = 3, every point represents y < 3 and y = 3
Horizontal and vertical regions combined
When combining horizontal and vertical regions, the unwanted regions are shaded out. This enables the required area to be easily identified.
In the graph above, the regions represent –4 < x < –1 and –1 < y ≤ 3.
The regions which are unshaded represent –4 < x < –1 and –1 < y ≤ 3.