10/11/22 - Periodic Functions

Question 1

What are periodic functions?

Answer 1

Functions that stay the same when shifted horizontally.

Question 2

What is the equation form for a periodic function?

Answer 2

f(x) = f(x + p), where p > 0. Here, p is the period of the function.

Question 3

Is a constant function a periodic function?

Answer 3

No

Question 4

For f(x) = f(x + 2), what is the period?

Answer 4

2

Question 5

For f(x) = (x + 6), how often does the function repeat?

Answer 5

Every 6 units (the period is 6)

Question 6

If a function’s period is 3, how do you find f(5) from f(8)?

Answer 6

They are the same. You can add and subtract 3 from the input, and the output will be the same.

Question 7

In a periodic function, what does M represent?

Answer 7

The function’s maximum y-value.

Question 8

In a periodic function, what does m represent?

Answer 8

The function’s minimum y-value.

Question 9

What is the equation for the midline of a periodic function?

Answer 9

y = 1/2(M + m)

Question 10

What is the equation for the amplitude of a periodic function?

Answer 10

Amplitude = 1/2(M - m)

Question 11

What is the amplitude of a periodic function?

Answer 11

The distance from the midline to the maximum or minimum.

Question 12

A function has a period of 4. Find f(26)

Answer 12

f(26) = f(2)
26/4 = 6 w/ a remainder of 2