A function $f$ on the set of real numbers is defined as
$$f ( x ) = \frac { | x | } { 1 + | x | }$$
Accordingly, which of the following is the image set of the interval $[ - 2,1 )$ under the function $\mathbf{f}$?\
A) $[ 0,1 ]$\
B) $\left( \frac { 1 } { 3 } , \frac { 2 } { 3 } \right]$\
C) $\left[ \frac { 1 } { 3 } , \frac { 2 } { 3 } \right)$\
D) $\left[ 0 , \frac { 1 } { 3 } \right]$\
E) $\left[ 0 , \frac { 2 } { 3 } \right]$