2023 SJI P1 Q3

A curve with equation \(y=\mathrm f(x)\) undergoes the following sequence of transformations.

A: A translation by \(\begin{pmatrix}-2\\1\end{pmatrix}\).

B: A reflection in the \(x\)-axis.

C: A horizontal stretch with scale factor \(\dfrac13\).

The resulting curve has equation \(y=\dfrac1{x-2}\).

1. Find an expression for \(\mathrm f(x)\).[4]
2. Sketch the graph of \(y=\dfrac1{x-2}\), indicating clearly the axial intercept and the equations of the asymptotes.[3]