Periodic expansion of function

Question

Let $ \tilde{f}: \mathbb{R} \rightarrow \mathbb{R} $ be the 2-periodic expansion of the function $ f: [-1,1[ \rightarrow \mathbb{R} $ given by $ f(x)=x $.

But how can I make a graph of $ \tilde{f} $ and how can I detemine $ \tilde{f}(3) $ and $ \tilde{f}(5)?$

I know I should use the formula $ \tilde{g}(x+np)=g(x) $.

Answer 1

You can plot it with WolframAlpha:

plot mod(x,2,-1), x=-4..4

In general mod(x, n), gives the remainder when $x$ is divided by $n$. When $n=2$, we'd expect something between $0$ and $2$. In the three argument form, mod(x,n,m), $m$ is an offset. Thus we get something between $m$ and $m+n$. In this case, something between $-1$ and $1$.