Sketch the curve \[y=\frac{(x-1)(x-4)}{(x-2)(x-3)}\] and also, using this curve if you wish and explaining your argument carefully, the curve \[y^2=\frac{(x-1)(x-4)}{(x-2)(x-3)}.\]

Sketch the curve \[y=\frac{(x-1)(x-4)}{(x-2)(x-3)}\] and also, using this curve if you wish and explaining your argument carefully, the curve \[y^2=\frac{(x-1)(x-4)}{(x-2)(x-3)}.\]