Sketch the graph of any cubic function that has both three distinct real roots and a negative coefficient of $x^3$.

The function $g(x)$ is defined by

where $a$ and $k$ are constants and $a>0$.

Show that there is a stationary point where the curve crosses the $y$-axis.

Given that the equation $g(x)=0$ has three distinct real roots, find the range of possible values for $k$ in terms of $a$ by considering the positions of the local maximum and local minimum points.