AHSME 1961 Problem 34

Let S be the set of values assumed by the fraction $\frac{2x+3}{x+2}$. When $x$ is any member of the interval $x \ge 0$. If there exists a number $M$ such that no number of the set $S$ is greater than $M$, then $M$ is an upper bound of $S$. If there exists a number $m$ such that such that no number of the set $S$ is less than $m$, then $m$ is a lower bound of $S$. We may then say: $\textbf{(A)}\ \text{m is in S, but M is not in S} \\ \textbf{(B)}\ \text{M is in S, but m is not in S} \\ \textbf{(C)}\ \text{Both m and M are in S} \\ \textbf{(D)}\ \text{Neither m nor M are in S} \\ \textbf{(E)}\ \text{M does not exist either in or outside S}$