# What's the Period of This Function?

Consider the following function defined on the interval $[0,\pi]$

$$f(t)=\left\{\begin{array}{ll}t^2,\quad&\mbox{for } -\pi\leq t<\pi, \\ f(t-2k\pi),\quad&\mbox{for } -\pi+2k\pi\leq t<\pi+2k\pi.\end{array}\right.$$

What is the period for this function? I'm trying to use the fourier series for this, but the formula requires knowing the period. My first guess is that the period is $2\pi$ because it's going from $-\pi$ to $\pi$, but the second part of the function throws me off. Please help?

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Try graphing it, for particular values of $k$. –  Javier Sep 2 '13 at 20:47
Your first guess is correct and the second part of the function says the same. –  njguliyev Sep 2 '13 at 20:55