Activity
The number of people who watched a TV episode is a function of that show’s episode number. Here are three graphs of three functions—, , and —representing three different TV shows.
Show A
Show B
Show C
Match each description with a graph that could represent the situation described. One of the descriptions has no corresponding graph.
1. This show has a good core audience. It had a guest star in the fifth episode that brought in some new viewers, but most of them stopped watching after that.
The graph of function
2. This show is one of the most popular shows, and its audience keeps increasing.
no match
3. This show has a small audience, but it’s improving, so more people are noticing.
The graph of function
4. This show started out huge. Even though it feels like it crashed, it still has more viewers than another show.
The graph of function
5. Which is greatest, , ,
6. Explain what the answer to question 5 tells us about the shows.
Compare your answer:
Your answer may vary, but here is a sample. 3.6 million people watched the 7th episode of Show B.
7. Use the Desmos graphing tool or technology outside the course to sketch a graph of the viewership of the fourth TV show that did not have a matching graph.
Compare your answer:
Video: Comparing Functions Represented in Separate Graphs
Watch the following video to learn more about how to compare functions that are represented in separate graphs.
Self Check
Additional Resources
Comparing Real-Life Functions
Two people, Adam and Bianca, are competing to see who can save more money in one month. Use the table and the graph below to determine who will save more money at the end of the month. State how much money each person had at the start of the competition. (Assume each is following a linear function in his or her saving habit.) Let Adam’s function be represented by , where is days, and Bianca’s function be represented by .
Which is greater, or ? Explain what this answer means.
and , so after 2 days, Adam has saved more money.
Try it
Try It: Comparing Real-Life Functions
Aleph is running at a constant rate on a flat, paved road. The graph below, , represents the total distance, , he covers with respect to time, .
Shannon is running on a flat, rocky trail that eventually rises up a steep mountain. The graph below, , represents the total distance, , she covers with respect to time, .
Who has traveled farther after 40 minutes? Explain your answer.
Here is how to determine who went a greater distance:
Aleph traveled farther in 40 minutes. Comparing the graphs, is 5.5 miles, and is approximately 2.5 miles.