1961 AMC 12 Question 34 - thichhoctoan.com

Question 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 $x\ge0.$ Let $M$ be the least upper bound of $S,$ and let $m$ be the greatest lower bound of $S.$ We may then say:

$m$ is in $S,$ but $M$ is not in
$S$
$M$ is in $S,$ but $m$ is not in $S$
both $m$ and $M$ are in $S$
neither $m$ nor $M$ is in $S$
$M$ does not exist either in or outside $S$