<ol class="abc-list"><li><div class="list-item-paragraph">The diagram below shows the graph of  $y=\mathrm{f}\left( x \right)$. The graph has a minimum point at $\left( 1,3 \right)$ and intersects the axes at $x=-2$and $y=4$.  The equations of the asymptotes are $y=2x$ and $x=-1$.</div><div class="graph-block" data-graph-config="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" data-width="275" data-height="225" style="width:275px;height:225px;max-width:100%;display:block;margin:0 auto;"></div><div class="list-item-paragraph">On separate diagrams, sketch the graphs of </div><ol class="i-list"><li><div class="list-item-paragraph">$y=\mathrm{f}'\left( x \right)$,<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">$y=\frac{1}{\mathrm{f}(x)}$,<span class="inline-marks">[2]</span></div></li></ol></li></ol>

The diagram below shows the graph of  $y=\mathrm{f}\left( x \right)$. The graph has a minimum point at $\left( 1,3 \right)$ and intersects the axes at $x=-2$and $y=4$.  The equations of the asymptotes are $y=2x$ and $x=-1$.

On separate diagrams, sketch the graphs of 

Transformations of Graphs - General

Transformations of Graphs

International Baccalaureate Higher Level Mathematics

2013 TJC P1 Q7

2013 TJC P1 Q7