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:

$\displaystyle 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)?