The diagram below shows a sketch of the curve \(y=\mathrm{f}(x)\).
\(y=\mathrm{f}'(x)\) and[3]
\(y=-\dfrac{1}{2}\mathrm{f}(x-1)\).[3]
For each sketch, state the equations of any asymptotes, and the coordinates of any points where the curve crosses the axes, turning points and points corresponding to \(A\) and \(B\), wherever possible.
A graph undergoes transformations in the following sequence.
Translation of 2 units in the negative \(y\)-direction.
Reflection in the \(y\)-axis.
Scaling parallel to the \(y\)-axis by a scale factor of 3.
The equation of the resultant graph is \(y^3=2x^2(x-1)\). Find the equation of the original graph.[3]
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