Question

Determine whether the function is periodic. If it is, find the period.

Answer 1

A. periodic; about 6

B. periodic; about 3

C. periodic; about 12

D. not periodic

Answer 2

Does the function repeat itself exactly? How far is the distance from the dirt time to the second?

Answer 3

I dont know

Answer 4

Well, I suggest you pick a point on the left side of the graph. Scan along the graph the see if that exact value of y appears again on the graph. If not, it is not periodic. If yes, see if the two graphs make identical moves from that point.

Answer 5

I think it is periodic, and it does make identical moves.

Answer 6

It does look like it's repeating itself... So, you agree, @ExplainItLikeImFive , so you can pick out one point, AND then find out where it's repeated in the pattern?

Answer 7

Yes

Answer 8

Okay! So how far away are those points? I mean, the point and where that point is repeated. The distance between them is the "period" and is the answer to your question.

Answer 9

About 6

Answer 10

I agree!
\(\huge\color{blue}{\large\ \ o\ o\ \\\smile}\)

Answer 11

Congratulations!

Answer 12

Thanks

Answer 13

Haha, you did the work. And thanks to @whpalmer4 for clearly introducing that great method to see if it was periodic!

Answer 14

The period of this function is probably \(2\pi\approx 6.28\) but of course that isn't an answer choice this time. Expect it to be in the future, however :-)

Answer 15

:)

Answer 16

I didn't give a full description of the method — if the next point at which you have the same y value doesn't behave identically, go to the next point which has a matching y value and try again. Keep trying until you run out of candidates, or find one that works. Probably obvious, but better safe than sorry...

Answer 17

Haha, I like the completion.