<p>The diagram below shows the graph of \(y=\mathrm{f}(x)\). The graph has asymptotes \(y=a+bx\) and \(x=0\), intersects the \(x\)-axis at the point \((c, 0)\) and has a turning point \((d, e)\).</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/1769316343120-d2gtkr9cpzr.png" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<p>Sketch the following graphs on separate diagrams, labelling the equations of any asymptotes and the coordinates of any points where the graphs cross the axes and of any turning points.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">\(y=3\mathrm{f}(x+c)\),</span><span class="inline-marks">[2]</span></div></li><li><div class="list-item-content"><span class="list-item-text">\(y=\frac{1}{\mathrm{f}(x)}\),</span><span class="inline-marks">[3]</span></div></li><li><div class="list-item-content"><span class="list-item-text">\(y=\mathrm{f}'(x)\).</span><span class="inline-marks">[2]</span></div></li></ol>

The diagram below shows the graph of \(y=\mathrm{f}(x)\). The graph has asymptotes \(y=a+bx\) and \(x=0\), intersects the \(x\)-axis at the point \((c, 0)\) and has a turning point \((d, e)\).

Sketch the following graphs on separate diagrams, labelling the equations of any asymptotes and the coordinates of any points where the graphs cross the axes and of any turning points.

Graphing Techniques

International Baccalaureate Higher Level Mathematics

2025 YIJC P1 Q6

2025 YIJC P1 Q6