\section*{4. A}
Solution: Based on the graph and properties of translation, the function $f ( x )$ is monotonically increasing on $\left( - \frac { \pi } { 3 } , \frac { 2 \pi } { 3 } \right)$ and monotonically decreasing on $\left( - \frac { 2 \pi } { 3 } , \frac { 5 \pi } { 3 } \right)$.