1961 AHSME 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:

\begin{array}{l} \textbf{(A)}\ \text{m is in S, but M is not in S}\qquad\\ \textbf{(B)}\ \text{M is in S, but m is not in S}\qquad\\ \textbf{(C)}\ \text{Both m and M are in S}\qquad\\ \textbf{(D)}\ \text{Neither m nor M are in S}\qquad\\ \textbf{(E)}\ \text{M does not exist either in or outside S} \end{array}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.