Prove that the limit of the function a sequence is the same as the function of the limit of the sequence

Question

Assume that $\lim_{n\to \infty}a_n=a.$ Suppose that the function $f$ is continuous everywhere including at $a$. Form the sequence $(f(a_n))_{n=1}^{\infty}$. Prove that $\lim_{n\to \infty}f(a_n)=f(\lim_{n\to \infty}a_n).$ So show $\lim_{n\to \infty}f(a_n)=f(a).$

Help me, I am lost on how to even begin.