Overview:

It is important to be able to describe the differences in behavior among various kinds of functions. Some functions, such as polynomial functions, have graphs that are unbroken. Their graphs can be drawn without lifting pencil from paper. Many functions do not share this property. For example, the graph of
y = 1/x has unusual behavior near x = 0: It cannot be graphed from x = -1 to x = 1 without lifting pencil from paper. Functions without any breaks or holes in their graphs are continuous. In this activity, you will explore the graphical behavior of continuous functions.

Materials:

• TI-84 Plus / TI-83 Plus

Activity:

Graphical Consequences of Continuity