A function $f$ is given by the function equation $f ( x ) = x ^ { 3 } - 3 x , x \in \mathbb { R }$.
The graph of $f$ is shown in the figure.
(1) Justify that the graph of $f$ is point-symmetric about the origin.
(2) The graph of $f$ encloses an area with the $x$-axis in the second quadrant. Determine the area $A$ of this region by calculation.
[For verification: $A = 2.25 \mathrm { FE }$.]
(3) Given is the line $g : y = - 2 x , x \in \mathbb { R }$. Determine the ratio in which the line $g$ divides the area from (2).