Skill check: Using limits

Let $\qquad f(x) = \begin{cases} 1+3\cos(2x) &\text{if $x<\pi$}\\ 4+\sin x &\text{if $x\geq \pi\,. $} \end{cases}$ Is $f$ continuous at the point $x=\pi$? Why? [[☃ radio 1]]