The graph of $y=\mathrm{f}\left( x \right)$ is shown below. On separate diagrams, sketch the follo

Question

The graph of $y=\mathrm{f}\left( x \right)$ is shown below. On separate diagrams, sketch the following graphs, indicating clearly the key features $y=\mathrm{f}\left( 1-x \right)$,[3] $y=\mathrm{f}'\left( x \right)$.[3] 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]

Accepted Answer

(a)(i) Graph shown, with vertical asymptotes $x=-1$ and $x=1$, horizontal asymptote $y=3$, and turning points $(0,-1)$ and $(3,1)$ (a)(ii) Graph shown, with vertical asymptotes $x=0$ and $x=2$, horizontal asymptote $y=0$, and zeros at $(-2,0)$ and $(1,0)$ (b) Reflect in the $x$-axis, then translate one unit in the negative $x$-direction

2021 RI P1 Q5

2021 RI P1 Q5

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