4.10.3 Comparing Functions Represented in Separate Graphs

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 $B(t)$.

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

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, $t$.

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, $t$.

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.