# Example QF.DQInEQ.0

- Author:
- Martin Flashman

Consider the quadratic function .
The key result on quadratic functions as compositions is very useful here for
visualizing how to solve an inequality of the form with by considering the related inequality
The mapping diagram for considered as a
composition helps visualize the inequality . as well as the solution set:
When the apping diagram has solution set .
, the solution set is ( .
When the mapping diagram helps visualize the solution set, .
the solution set is ( .
In the case, the diagram visualizes why the solution set is , and when the
diagram visualizes why the solution set is empty.

**For example,**for the inequality**For example***,*for the inequality