<ol class="abc-list"><li><div class="list-item-paragraph">The graph of $y=\mathrm{f}(x)$ is shown in the diagram. It passes through the origin and has a minimum point at $\left( 2,\mathrm{ }0 \right)$. The lines $x=1$ and $y=2$ are the asymptotes of the graph.</div><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/converted/1759755650243-f34pm5sc6li.png" alt="List item image" class="aligncenter custom-width" style="max-width: min(450px, 100%); height: auto;" /></div><div class="list-item-paragraph">Sketch the graph of $y=2-\mathrm{f}(x)$, stating the coordinates of the point where the graph crosses the $y$-axis, the coordinates of any stationary point(s) and the equations of any asymptotes.<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">The curve $C$ has equation $y=\frac{2{{x}^{2}}+kx-2}{x+2}$, where&nbsp;$k$ is a constant.</div><ol class="i-list"><li><div class="list-item-paragraph">Find the set of values of $k$ for which $C$ has&nbsp;$2$ stationary points.<span class="inline-marks">[3]</span></div><div class="list-item-paragraph">For the rest of the question, take $k=-3$.</div></li><li><div class="list-item-paragraph">By expressing the equation $y=\frac{2{{x}^{2}}-3x-2}{x+2}$ in the form $y=ax+b+\frac{c}{x+2}$, where&nbsp;$a$, $b$ and $c$ are constants, write down the equations of the asymptotes of $C$.<span class="inline-marks">[3]</span></div></li><li><div class="list-item-paragraph">Hence sketch $C$, giving the equations of any asymptotes, the coordinates of any stationary points and of the points where&nbsp;$C$ crosses the axes.<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">Describe a pair of transformations which transform the graph of $y=x+\frac{6}{x+2}$ to $C$.<span class="inline-marks">[2]</span></div></li></ol></li></ol>

The graph of $y=\mathrm{f}(x)$ is shown in the diagram. It passes through the origin and has a minimum point at $\left( 2,\mathrm{ }0 \right)$. The lines $x=1$ and $y=2$ are the asymptotes of the graph.

Sketch the graph of $y=2-\mathrm{f}(x)$, stating the coordinates of the point where the graph crosses the $y$-axis, the coordinates of any stationary point(s) and the equations of any asymptotes.

The curve $C$ has equation $y=\frac{2{{x}^{2}}+kx-2}{x+2}$, where $k$ is a constant.

2020 VJC Promo Q8

2020 VJC Promo Q8

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