Which of the following statements must be true, given the limit $\mathop {\lim}\limits_{x \to \infty}f(x)=3$?

I.$f(c) \ne 3$ for all values of $c$ in the domain of $f$II.$x=3$ is a vertical asymptote for the graph of $f(x)$III.$y=3$ is a horizontal asymptote for the graph of $f(x)$