Which one of the following statements is true?
\correct Any uniformly continuous function on $(2,7)$ is bounded.
\wrong Any bounded continuous function on $(2,7)$ is uniformly
continuous.
\wrong Any one-to-one (i.e. injective) continuous function on $(2,7)$ is bounded.
\wrong If $f(x)$ is continuous on $(2,7)$ then there exists $x\in(2,7)$
with $f(x)=5$.
\wrong if $f(x)$ is continuous on $(2,7)$ then there exists a
sequence $(x_n)$ of points from $(2,7)$ such that $\lim x_n=2$ and
$\{f(x_n):n\ge0\}$ is bounded.