Work Step by Step
Note that $f(0)=f(3)$, $f(1)=f(4)$, and $f(2)=f(5)$. Therefore, it can be speculated that $f(x)=f(x+3)$. Since there exists an $a$ such that $f(x)=f(x-a)$, this function is periodic with period of $3$.
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