2023 RI P1 Q4

Describe a sequence of transformations that will map the graph of \(y=\mathrm{f}\left( x \right)\) onto the graph of \(y=1-2\mathrm{f}\left( x \right)\).[3]

A point \(P\left( a,b \right)\) is said to be \(R\)-invariant if it lies on both the graphs of \(y=\mathrm{f}\left( x \right)\) and \(y=\frac{1}{\mathrm{f}\left( x \right)}\).

Sketch the graph of a function \(y=\mathrm{f}\left( x \right)\), which is defined for all real \(x\), for which \(\mathrm{{f}'}\left( x \right)<0\) for all real \(x\) and there are no \(R\)-invariant points.[2]