Let's take a look at the axes of the given coordinate plane.

We begin by identifying the independent and dependent variables. Since Time is on the

x -

axis, it is the independent variable. Likewise, since Total People is on the

y -

axis, it is the dependent variable.

Independent Variable : Dependent Variable : Time Total People

Next, we think of a scenario where the total number of people depends on the time. We are also given that this function must have at least two different intervals, so we might think of a place that fills up with people for some time and then empties out.

Let's use a movie theater! People gradually come into the theater to take their seats before the movie begins. This is shown as a small interval where the function is $increasing .$

Total people vs time increasing interval

After the movie starts, everyone stays in their seats for the duration of the movie. This is represented by a longer interval where the function is $constant .$

Total people vs time increasing and constant intervals

After the movie ends, people start to leave the movie theater. This is shown as a small interval where the function is $decreasing .$

Total people vs time increasing, decreasing, and constant intervals

Note that this is just one example of a function describing a total number of people in a place as a function of time. We can also consider the number of people in a stadium, students in a classroom, or even users on a streaming service. The list goes on and on!

Exercise