1. Algebra 2 12.6 Day 2 Notes Circular and Periodic Functions

2. Periodic Function A periodic function has y-values that repeat at regular intervals. One complete pattern is a cycle, and the horizontal length of one cycle is a period.

3. Example 1 Determine the period of the function.

4. Example 2 Determine the period of the function.

5. Example 3 Determine the period of the function.

6. Example 4 The pedals on a bicycle rotate as the bike is being ridden. The height of a bicycle pedal varies periodically as a function of the time, as shown in the figure. Notice that the pedal makes one complete rotation every two seconds. Make a table showing the height of a bicycle pedal at 3.0, 3.5, 4.0, 4.5, and 5.0 seconds. Identify the period of the function.

7. Example 4 Continued Graph the function. Let the horizontal axis represent the time t and the vertical axis represent the height h in inches that the pedal is from the ground.

8. Example 5 The pedals on a trick oversized bicycle rotate as the bike is being ridden. The height of a bicycle pedal varies periodically as a function of the time, as shown in the figure. Notice that the pedal makes one complete rotation every 4.0 seconds. Choose the correct table showing the height of a bicycle pedal at 0.0, 1.0, 2.0, 3.0, and 4.0 seconds. Identify the period of the function.

9. Example 5 Continued Find the maximum height and minimum height of the graph of the function if the horizontal axis represents the time t and the vertical axis represents the height in inches that the pedal is from the ground.

10. Exit Slip Determine the period of the function.