In Try This 3 you will explore how a composite function can be used to solve a problem.

 

Try This 3

 

Recall the scenario from the beginning of the lesson where a delivery truck regularly travels across a large city from its store to its warehouse. Suppose that someone tries to model this scenario and produces the following three graphs:

 

This is Graph 1.

 

 

This is Graph 2.

 

 

This is Graph 3.

1.  
   1. Describe the information Graph 1 contains. How does its shape relate to the scenario?
   2. Describe the information Graph 2 contains. How does its shape relate to the scenario?
2.  Use Graphs 1 and 2 to determine the time taken to drive across town at the following times:
   1. 2 h after midnight
   2. 8 h after midnight
   3. 24 h after midnight
3. Use Graphs 1 and 2 to determine a time after midnight when it would take 1 h to travel across town.
4. Graph 3 shows the composition of the function in Graph 2 with the function in Graph 1.
   1. What information does Graph 3 contain? How does its shape relate to the scenario?
   2. Give Graph 3 an appropriate title and label the horizontal and vertical axes.
5.  
   1. Explain how Graph 3 can be used to determine the times from question 2.
   2. Explain how Graph 3 can be used to determine the time from question 3.
6. Explain how Graph 3 could be drawn using Graphs 1 and 2.

Save your responses in your course folder.

 

Share 3

 

With a partner or group, discuss the following questions based on the information in Try This 3.

1. Describe any advantages or disadvantages of using a composition of functions to model the scenario in Try This 3.
2. Explain how realistic you feel the model in Try This 3 is. Describe any problems you see with the model.

If required, save a record of your discussion in your course folder.