A thin rod of length ' $L$ ' is lying along the $x$-axis with its ends at $x = 0$ and $x = L$. Its linear density (mass/length) varies with $x$ as $k\left( \frac { x } { L } \right) ^ { n }$, where $n$ can be zero or any positive number. If the position $x _ { \mathrm { CM } }$ of the centre of mass of the rod is plotted against ' $n$ ', which of the following graphs best approximates the dependence of $x _ { \mathrm { CM } }$ on $n$?
(1), (2), (3), (4) [see graphs in original]