6. Sketch Functions from Verbal Descriptions
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Think of a real-life scenario where the amount of people in a place changes over time.
See solution.
Let's take a look at the axes of the given coordinate plane.
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.
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.
After the movie ends, people start to leave the movie theater. This is shown as a small interval where the function is decreasing.
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!