Comparing Functions Represented in Separate Graphs

4.10.3 Comparing Functions Represented in Separate Graphs

4.10.3 • Comparing Functions Represented in Separate Graphs

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— $A$ , $B$ , and $C$ —representing three different TV shows.

Show A

Line graph showing audience in millions increasing steadily from episode 1 to episode 10, with both axes labeled. Audience starts below 0.5 million and ends at nearly 2 million.

Show B

A scatter plot showing audience in millions vs episode number. Audience starts at 9 million for episode 1 and gradually declines to about 3 million by episode 10.

Show C

A scatter plot showing audience in millions for episodes 1 to 10. Audience stays around 3 million, peaks at episode 6 with nearly 5.5 million, then returns to around 3 million for later episodes.

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 $C$

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 $A$

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 $B$

5. Which is greatest, $A (7)$ , $B (7)$ , $C (7)$

$B (7)$

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 $7^{th}$ 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.

Access multimedia content

Compare your answer:

Scatter plot showing audience in millions (y-axis) increasing with episode number (x-axis) from 1 to 10, indicating a rising trend in viewership as episodes progress.

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.

Access multimedia content

Self Check

For which of the following functions is

f(3)

the greatest value?

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 $A (t)$ , where $t$ is days, and Bianca’s function be represented by $B (t)$ .

A line graph titled Adam's Savings shows total savings in dollars on the y-axis and number of days on the x-axis. The line starts with $3 and rises steadily to $11 by day 3.

A line graph titled Bianca’s Savings shows a straight, upward-sloping orange line indicating total savings in dollars increasing steadily over several days. The x-axis is labeled Number of Days and the y-axis Total Amount of Money in Dollars.

Which is greater, $A (2)$ or $B (2)$ ? Explain what this answer means.

$A (2) = 9$ and $B (2) = 8$ , so after 2 days, Adam has saved more money.

Try it

Comparing Real-Life Functions

Aleph is running at a constant rate on a flat, paved road. The graph below, $A (t)$ , represents the total distance, $A$ , he covers with respect to time, $t$ .

Graph that shows total distance in miles as a function of time in minutes the graph is a straight line that increases from left to right and passes through the point (40, 5.5).

Shannon is running on a flat, rocky trail that eventually rises up a steep mountain. The graph below, $S (t)$ , represents the total distance, $S$ , she covers with respect to time, $t$ .

Graph that shows total distance in miles as a function of time in minutes. The graph is nonlinear and increases from left to right and includes the point (40, 2.5).

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, $A (40)$ is 5.5 miles, and $S (40)$ is approximately 2.5 miles.