2020 SJI P1 Q6

The graph of a polynomial function \(y=\mathrm{f}(x)\) is shown below. The curve cuts the \(x\)-axis at \(x=-3\) and \(x=7\), cuts the \(y\)-axis at \(y=2\), and has a maximum point at \((5,5)\).

Diagram is not drawn to scale.

1. On the set of axes below, sketch the graph of \(y=\dfrac1{\mathrm{f}(x)}\), labelling its asymptotes, turning points, and axial intercepts clearly.[5]

2. On the set of axes below, sketch the graph of \(y=(\mathrm{f}(x))^2\), labelling its turning points and axial intercepts clearly.[4]