Exploring the characteristics of periodic functions
About this video
A table shows three full cycles of a periodic function q with x going up by 0.5 each row. The video finds that the outputs repeat every time x increases by 1.5, so the period is 1.5, and fills each missing output by copying the value 1.5 units of x earlier.
You'll be able to
- find the period of a function from a table of values.
- use the period to fill in missing outputs of a periodic function.
Key words
- periodic function
- A function whose outputs repeat in the same pattern over and over.
- period
- The smallest change in x after which the outputs start repeating.
- cycle
- One complete repeat of the pattern of a periodic function.
Transcript
- [Instructor] The table shows three full cycles of the periodic function q. Complete the table for the missing outputs. Pause a video, have a go at that. All right, so let's see what's going on here. So x, and it looks like x is increasing by exactly 0.5 by half every time.
And this is three full cycles. So it looks like one full cycle. There's a couple of ways we could think about it here, is that they're giving us a total of nine entries here, I guess you could say. So maybe there's some type of a pattern we could see like that.
Or another way to think about it is it looks like every time x increases by 1.5, we get back to where we started. So that looks like we have completed one full period. And so if we increase x by 1.5 again, we should complete another full period. So we should get back to where we were for q.
So we start at four, after a period we get back to four. After another period, we should get back to four. All right, well we could do that same idea again. You start at 2.5, add 1.5, you get to four, and we should get back to that same value, 2, -2. And you add 1.5 again, we should get to -2 again, which is indeed what happened.
And then last but not least, okay, what is this missing value? Well, it should be the same as whatever we get after adding 1.5 to x. So it should be the same as that, which should be the same as that, which are both equal to one and we're done.
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