2.4 Graphing inequalities

In general, the graph of an inequality is a shaded area .

Consider the graph $y=\mid x\mid$ shown above. Every point on that V-shape has the property that its $y$ -value is the absolute value of its $x$ ­ -value . For instance, the point $(-\mathrm{3,3})$ is on the graph because 3 is the absolute value of –3.

The inequality $y<\left|x\right|$ means the $y$ -value is less than the absolute value of the $x$ -value . This will occur anywhere underneath the above graph. For instance, the point $(-\mathrm{3,1})$ meets this criterion; the point $(-\mathrm{3,4})$ does not. If you think about it, you should be able to convince yourself that all points below the above graph fit this criterion.

The dotted line indicates that the graph $y=\mid x\mid$ is not actually a part of our set. If we were graphing the line would be complete, indicating that those points would be part of the set.