I have to give an answer to an assignment question and I don't know where to start. I would prefer the direction of how to solve it instead of an explicit answer since I have no work done on it yet.

Let $f$ be a continuous real-valued function on $\mathbb{R}$ with the property that for each real number $x$, $\lim_{n\rightarrow \infty} f(nx)=0$. Show that $\lim_{x\rightarrow \infty} f(x) = 0$.

Thank you!