= Solution
Successive jumps occur at times separated by \b[$T=6$ s]. Between $-3$ and $3$ s the plotted function is $f(t)=2-t$, periodically extended, with maximum $5$ and minimum $-1$. Its mean is therefore \b[$2$ m], and $f(t)-2=-t$ is an <odd function> over that centered period.
For the <Fourier series> convention
$$
f(t)=\frac{a_0}{2}+\sum_{r=1}^{\infty}
\left[a_r\cos\frac{2\pi rt}{T}+b_r\sin\frac{2\pi rt}{T}\right],
$$
\b[$a_0=4$ m and $a_r=0$ for every $r\ge1$]; the nonconstant content consists of <sine> terms. If $a_0$ denotes the mean directly in the alternative convention $f=a_0+\sum\cdots$, its value is $2$ m. Stating the convention resolves the otherwise ambiguous notation.
For completeness, integrating $-t$ against the <sine> basis gives \b[$b_r=6(-1)^r/(\pi r)$ m]. At a jump the <Fourier series> converges to the midpoint $2$ m. The nonzero mean does not destroy the oddness argument for the mean-subtracted function; declaring the original function itself odd would incorrectly force its mean to vanish.
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