Extra #1

Continuous graphs vs. Discrete graphs

When we talk about functions, there are really two different types of graphs: continuous and discrete. We need to be able to tell the difference.

A continuous graph is made up of connected dots, but a discrete graph is made up of individual points. Consider the following two examples to see the difference.

Example 1: An example of a discrete graph could be a graph of attendance at a theme park. Because each year is distinct, each year has only one value. We do NOT connect the dots because the values between whole numbers have no meaning for this situation. In other words, we would have data for the year 2010 and 2011, but since there isn't a year in between these two years, we shouldn't connect the dots.

Example 2: An example of a continuous function could be a graph of how the temperature changes throughout the day. Unlike Example 1, we always have a corresponding temperature for any given time. In other words, we have data for 1:00 and 2:00, but we also have data for 1:01, 1:02, 1:03, etc. If we wanted to keep going, we also have data for the 60 seconds in between 1:01 and 1:02, and so on.