<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="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1769597765170-cebjx0p9my7.png" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<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">$y=\mathrm{f}\,\text{}\hspace{0.5em}\!\!'\!\!\text{}\hspace{0.5em}\left( x \right)$.</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 

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

$y=\mathrm{f}\,\text{ }\!\!'\!\!\text{ }\left( x \right)$.

Transformations of Graphs - General

Transformations of Graphs

H2 Math

International Baccalaureate Higher Level Mathematics

2015 JJC P1 Q8

2015 JJC P1 Q8