# Thread: Quick Periodic Extension Question

1. ## Quick Periodic Extension Question

If you were asked to do a periodic extension of a function and to increase the period, would you stretch the parameters out?

For example:
$f(x)=\left\{\begin{array}{cc}x^2,&\mbox{ if }
[0,1)\\2-x, & \mbox{ if } [1,2]\end{array}\right.$

If were told to do a periodic extension, but change the period from 2 to 4, how would I go about doing this? Would I change the first interval from [0,1) to [0,2)?

2. Originally Posted by BlackBlaze
If you were asked to do a periodic extension of a function and to increase the period, would you stretch the parameters out?

For example:
$f(x)=\left\{\begin{array}{cc}x^2,&\mbox{ if }
[0,1)\\2-x, & \mbox{ if } [1,2]\end{array}\right.$

If were told to do a periodic extension, but change the period from 2 to 4, how would I go about doing this? Would I change the first interval from [0,1) to [0,2)?
Look closely this picture.

I think that is understandable.

In the general case (on the real line) for your function $k \in \mathbb{Z}$

3. Wait.
Wait, wait, wait, wait.

...Nope, I lost it. Forgive me, I guess I'm not that bright. I see you were able to make a simple periodic extension of my function, but I do not understand how the k plays a part. Am I to extend function so that when k = 0, f(x) can go across 0->4?