✓ Got It?

1. Analyze each periodic function. Identify the cycle in two different ways. What is the period of the function?
   1. 
   2. 

Problem 2 Identifying Periodic Functions

Is the function periodic? If it is, what is its period?

1. 

   Although the graph shows similar curves, the y-values from one section do not repeat in other sections. The function is not periodic.

2. 

   The pattern of y-values in one section repeats exactly in other sections. The function is periodic.

   

   Find points at the beginning and end of one cycle. Subtract the x-values of the points: 10 − 0 = 10 . 10 minus 0 equals 10 .  The pattern in the graph repeats every 10 units, so its period is 10.

✓ Got It?

2. Is the function periodic? If it is, what is its period?
   1. 
   2. 
   3. Reasoning If the period of a function is 4 seconds, how many cycles does it have in a minute? What is the period of a function that has 180 cycles per minute (for example, a point on a spinning wheel)? That has 440 cycles per second (for example, a point on the end of a tuning fork)?