(a) The graph of $y=\mathrm{f}(x)$ is shown below.

On separate diagrams, sketch the following graphs, indicating clearly the key features.

(i) $y=\mathrm{f}(1-x)$,

[3]

(ii) $y=\mathrm{f}^{\prime}(x)$.

[3]

(b) State a sequence of transformations which transform the graph of $y=\ln \left(1-\frac{x}{2}\right)$ onto the graph of $y=\ln \left(\frac{2}{1-x}\right)$.

[3]

(a)(i)

(a)(ii)

(b) Scale the graph of \(y=\ln \left(1-\frac{x}{2}\right)\) parallel to the \(x\)-axis by factor \(\frac{1}{2}\), followed by a reflection about the \(x\)-axis, followed by a translation of \(\ln 2\) units in the positive \(y\) direction.

Reflect the graph of \(y=\ln \left(1-\frac{x}{2}\right)\) about the \(x\)-axis, followed by a translation of 1 unit in the negative \(x\)-direction.