1. (a) Describe fully the single transformation that maps the graph of \(y = \mathrm { f } ( x )\) onto the graph of \(y = \mathrm { f } ( x - 1 )\).
   (b) Showing the coordinates of any points of intersection with the coordinate axes and the equations of any asymptotes, sketch the graph of \(y = \frac { 1 } { x - 1 }\).
   (c) Find the \(x\)-coordinates of any points where the graph of \(y = \frac { 1 } { x - 1 }\) intersects the graph of \(y = 2 + \frac { 1 } { x }\). Give your answers in the form \(a + b \sqrt { 3 }\), where \(a\) and \(b\) are rational.
2. A store begins to stock a new range of DVD players and achieves sales of \(\pounds 1500\) of these products during the first month.

In a model it is assumed that sales will decrease by \(\pounds x\) in each subsequent month, so that sales of \(\pounds ( 1500 - x )\) and \(\pounds ( 1500 - 2 x )\) will be achieved in the second and third months respectively. Given that sales total \(\pounds 8100\) during the first six months, use the model to