Periodic Functions

Periodic Data

Lesson 13-1

What is a periodic function?

A periodic function is a function that repeats a pattern of y-values (outputs) at regular intervals.

Cycles

One complete pattern is a cycle. A cycle can begin on any point on the graph of the function.

Multiple Choice

Is this a periodic function?

• Yes

• No

Yes

This function is periodic because it follows a regular pattern.

Period of a function

The period is the horizontal length (the distance along the x-axis) of one cycle.

Amplitude of function

 $amplitude\ =\ \frac{1}{2}\left(\max-\min\right)$  The amplitude measures the amount that the function values variate. The amplitude is half of the difference between the minimum and maximum.

Check out this periodic function

Multiple Choice

What is the Period of this function?

• 1

• $$\pi$$

• I don't know

• You've gone too far

Multiple Choice

What is the amplitude of this function?

• 0

• 1

• $$\pi$$

• Definitely not this one

Multiple Choice

A Periodic Function goes through 5 complete cycles in 4 minutes. What is the period of the function?

• 1/5 min

• 1/4 min

• 48 s

• 75 s

Multiple Choice

The period of a periodic function is 8s. How many cycles does it go through in 30s?

• 4/15 cycles

• 3.75 cycles

• 22 cycles

• 240,567,849 cycles

Multiple Choice

The amplitude of a periodic function is 2.5 and its minimum values is 0. What is the functions maximum value?

• -2.5

• 0

• 2.5

• 5

Multiple Choice

The amplitude of a periodic function is -2.5 and its maximum value is 0. What is the functions minimum value?

• 2.5

• 0

• -2.5

• -5