N2007 P1 Q5

Show that the equation \(y=\frac{2x+7}{x+2}\) can be written as \(y=A+\frac B{x+2}\), where \(A\) and \(B\) are constants to be found. Hence state a sequence of transformations which transform the graph of \(y=\frac1x\) to the graph of \(y=\frac{2x+7}{x+2}\).[4]

Sketch the graph of \(y=\frac{2x+7}{x+2}\), giving the equations of any asymptotes and the coordinates of any points of intersection with the \(x\)- and \(y\)-axes.[3]