fourier series sketching (by hand)

Question

I calculated the Fourier Series representation of $f (x) = 1 − |x|$ on $−1 ≤ x ≤ 1$ and now I am asked to sketch the graph of the series on $−3 ≤ x ≤ 3$ by hand. How do I do this? I read through my lecture notes and find it very confusing. In my notes, all the axis of graphs are using $x$ over $\pi$ or $y$ over $\pi$, is that always the case when I come across with rage involving $\pi$?

Answer 1

The sum of the series is the periodic extension (of period $2$) of $f$. All you have to do is copy the graph of $f$ on $[-1,1]$ on $[1,3]$ and $[-3,-1]$.