Consider the function $f : R \rightarrow R$ defined by $f ( x ) = \left\{ \begin{array} { c c } \left( 2 - \sin \left( \frac { 1 } { x } \right) \right) | x | , & x \neq 0 \\ 0 , & x = 0 \end{array} \right.$. Then $f$ is:\\
(1) monotonic on $( - \infty , 0 ) \cup ( 0 , \infty )$\\
(2) not monotonic on $( - \infty , 0 )$ and $( 0 , \infty )$\\
(3) monotonic on $( 0 , \infty )$ only\\
(4) monotonic on $( - \infty , 0 )$ only