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Let $Per(\\phi,K)$, $PrePer(\\phi, K)$, and $Tail(\\phi,K)$ be the set of $K$-rational periodic, preperiodic, and purely preperiodic points of $\\phi$, respectively. The present paper presents two main results. The first result gives a bound for $|PrePer(\\phi,K)|$ in terms of the number of places of bad reduction $|S|$ and the degree $d$ of the rational function $\\phi$. 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