Another Example of A Piecewise Function - Ping Response Times

The 7th and 8th Graders are doing a project on piecewise functions. Piecewise functions are ubiquitous. Any time there is a dramatic, sudden change in a process you have a piecewise function. The graphs below show two stylized, textbook examples.

Here is a real world example from the world of IT from the PingER Project at Stanford.

The graphs below show how internet response rates change due to congestion. The change in response times is not just non-linear.  There is in fact a discontinuous break in the pattern,  There are two different set of rules governing response rates when the network is not congested and when it is congested.

Students interested in computers could very easily find similar examples of research in IT that shows similar types of discontinuities.