9 A curve \(C\) has equation
$$y = \frac { ( x + 1 ) ( x - 3 ) } { x ( x - 2 ) }$$
- Write down the coordinates of the points where \(C\) intersects the \(x\)-axis. (2 marks)
- Write down the equations of all the asymptotes of \(C\).
- Show that, if the line \(y = k\) intersects \(C\), then
$$( k - 1 ) ( k - 4 ) \geqslant 0$$
- Given that there is only one stationary point on \(C\), find the coordinates of this stationary point.
(No credit will be given for solutions based on differentiation.)
- Sketch the curve \(C\).