Let $f : \mathbb{R} \rightarrow \mathbb{R}$ be a function such that $f(x+1) = f(x)$ for all $x \in \mathbb{R}$. Which of the following statement(s) is/are true?\\
(A) $f$ is bounded.\\
(B) $f$ is bounded if it is continuous.\\
(C) $f$ is differentiable if it is continuous.\\
(D) $f$ is uniformly continuous if it is continuous.