How do I periodically extend a function?

Question

I am given that $f(x) = -1-x$ on $[-1,1)$ and I'm asked to find the Fourier series for the $2$ period extension of $f(x)$. I get how to find a Fourier series for the given function on the given interval. From some googling I understand what an odd and even extension are, but what is an extension by a set amount of periods? Even and odd extensions are infinite extensions from my understanding.

Answer 1

“2 period extension” doesn't mean that there are two periods, it means that the period is $T=2$.

Answer 2

Every real number $x$ belongs to $[2n-1,2n+1)$ for a unique integer $n$. For such an $x$ define $F(x)=f(x-2n)$. This is a function defined on the whole line with period $2$ and it coincides with $f$ on $[-1,1)$.