<p>The diagram below shows the curve with equation $y=\mathrm{f}\left( x \right)$ which has vertical asymptotes $x=a$ and $x=-a$ where&nbsp;$a&gt;0,$horizontal asymptote $y=0$ and a stationary point at $\left( 0,-1 \right)$.</p>
<div class="graph-block" data-graph-config="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" data-width="400" data-height="350" style="width:400px;height:350px;max-width:100%;display:block;margin:0 auto;"></div>
<p>Sketch, on separate diagrams, the graphs of </p>
<ol class="abc-list"><li><div class="list-item-paragraph">$y=\frac{1}{\mathrm{f}\left( x \right)}$,</div></li><li><div class="list-item-paragraph">$y=\mathrm{f}'\left( x \right)$.</div></li></ol>

The diagram below shows the curve with equation $y=\mathrm{f}\left( x \right)$ which has vertical asymptotes $x=a$ and $x=-a$ where $a>0,$horizontal asymptote $y=0$ and a stationary point at $\left( 0,-1 \right)$.

Sketch, on separate diagrams, the graphs of 

$y=\frac{1}{\mathrm{f}\left( x \right)}$,

Transformations of Graphs - General

Transformations of Graphs

International Baccalaureate Higher Level Mathematics

2015 JJC P1 Q8

2015 JJC P1 Q8