A curve \(C\) has equation \(y = \frac{ax^2 + x - 1}{x - 1}\), where \(a\) is a positive constant.

1. Find the equations of the asymptotes of \(C\).
2. Show that there is no point on \(C\) for which \(1 < y < 1 + 4a\).
3. Sketch \(C\). You do not need to find the coordinates of the intersections with the axes.