2024 MI PRU2 P1 Q2

The diagram shows the graph of \(y = \mathrm{f}(x)\) with asymptotes \(x = 0\) and \(y = 2x - 1\). The graph has a turning point at \(\left(2, \frac{21}{4}\right)\) and it cuts the \(x\)-axis at \(x = a\) where \(a < 0\).

1. Sketch the graph of \(y = \mathrm{f}'(x)\), stating the equations of any asymptotes and the coordinates of any turning points and points of intersection with the axes.[3]
2. The curve \(y = \mathrm{f}(x)\) undergoes the transformations \(A\), \(B\) and \(C\) in succession.
   
   \(\qquad A\): A translation of \(2\) units in the negative \(x\)-direction.
   \(\qquad B\): A stretch parallel to the \(y\)-axis with scale factor \(2\).
   \(\qquad C\): A translation of \(1\) unit in the positive \(y\)-direction.
   
   Find the equations of the asymptotes of the resulting curve.[3]