<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">The curve $C$ has equation $y=\frac{{{x}^{2}}-5x+7}{4-2x}$.</span></div><div class="list-item-paragraph">By expressing the equation of $C$ in the form $y=A\left[ \left( 3-x \right)+\frac{1}{\left( 3-x \right)+B} \right]$, where $A$ and $B$ are constants to be found, find a sequence of transformations which transforms the graph of $C$ on to the graph of $y=x+\frac{1}{x-1}$.</div><p style="text-align: right;">[4]</p></li><li><div class="list-item-content"><span class="list-item-text">The diagram below the graph of $y=\mathrm{f}\left( x \right)$ with an asymptote $x=0.5$. The curve passes through the origin $O$ and has only one stationary point at $\left( 1,2 \right)$. Sketch the graph of $\frac{1}{\mathrm{f}\left( x \right)}$, showing clearly the equations of any asymptotes and the coordinates of any turning points and $x$- intercepts.</span></div><p style="text-align: right;">[3]</p></li></ol>
<figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/converted/1759145245545-vssl1bmpsvk.png" width="400" class="aligncenter" /></figure>

The curve $C$ has equation $y=\frac{{{x}^{2}}-5x+7}{4-2x}$.

By expressing the equation of $C$ in the form $y=A\left[ \left( 3-x \right)+\frac{1}{\left( 3-x \right)+B} \right]$, where $A$ and $B$ are constants to be found, find a sequence of transformations which transforms the graph of $C$ on to the graph of $y=x+\frac{1}{x-1}$.

The diagram below the graph of $y=\mathrm{f}\left( x \right)$ with an asymptote $x=0.5$. The curve passes through the origin $O$ and has only one stationary point at $\left( 1,2 \right)$. Sketch the graph of $\frac{1}{\mathrm{f}\left( x \right)}$, showing clearly the equations of any asymptotes and the coordinates of any turning points and $x$- intercepts.

2020 ASRJC P1 Q4

2020 ASRJC P1 Q4

Video Solution:

Solution:

Handwritten & Typed Solutions