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Let $f$ be a periodic function with period $5$. The table below shows some input and corresponding output values of $f$. $$\begin{array}{|cccccccc|}\hline x& -1.5& -1& 0& 1& 2& 3& 4\\ f(x)& 0& 4& 1& -1& 3& 2& 4\\ \hline\end{array}$$ Identify which of the following statements is false.