2013 HCI Promo Q11

Sketch the graph of \(y=\frac{2{{x}^{2}}-3}{x-2}\), showing clearly the axial intercepts, the stationary points and the equations of the asymptotes where applicable.[3]

1. Solve the inequality \({\frac{2{{x}^{2}}-3}{x-2}\ge 1}\).[2]
   Deduce the solution of the inequality \(\frac{2{{\sin }^{2}}x-3}{\sin x-2}\ge 1\), where \(0\le x\le 2\pi \).[2]
2. Describe fully a sequence of transformations which would transform the graph of \(y=2x+\frac{5}{x}\) to the graph of \(y=\frac{2{{x}^{2}}-3}{x-2}\).[3]