A Survey of Mathematics Related Topics: Pg. 326, Example 1

This activity looks at graphs of possibly real life situations and asks you to decide if the graph makes sense in that context.

The main idea here is that graphs showing the relationships between two quantities, like time and speed for an aircraft, have certain laws that they have to follow. For example, speed doesn't change instantly -- if we are going 10 mph and then later we have sped up to 20 mph, sometime in the middle we have to be going 15 mph.

Ask yourself whether the graph is a function or not. If the graph is a function, does it necessarily make sense in the context of a real-life situation? What about the inverse of that statement -- if the graph is not a function does it necessarily not make sense in the context of a real-life situation?

The graphs shown here all relate two common everyday quantities. Judge which are possible in context and which are not.