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Discuss the continuity of:$$f(x)=\begin{Bmatrix} \cos(x)\quad & x<-\pi \\\ |\cos(x)| & -\pi \le x\le \frac { \pi }{ 2 } \\\ { \cos }^{ 2 }(x) & x>\frac { \pi }{ 2 } \end{Bmatrix}$$

$f(x)$ is has a jump discontinuity at $x=\cfrac {\pi }{2}$.

$f(x)$ is continuous on $[-2\pi , 0]$.

$f(x)$ is continuous on $[-\pi , \pi ]$.

$f(x)$ is continuous for all real numbers.