<p>The diagram below shows a sketch of the graph of \(y = \mathrm{f}(x)\). The curve passes through the points with coordinates \((1, 0)\) and \((3, 0)\), and has turning points at \((1, 0)\) and \((4, 4)\). The asymptotes are \(x = 0\), \(x = 2\) and \(y = 2\).</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/1769229443805-35d2cy6dxb1.png" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">The diagram below shows a sketch of the graph of \(y = \mathrm{f}(x)\). The curve passes through the points with coordinates \((1, 0)\) and \((3, 0)\), and has turning points at \((1, 0)\) and \((4, 4)\). The asymptotes are \(x = 0\), \(x = 2\) and \(y = 2\).</span></div><ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Sketch on separate diagrams, the graphs of \(y = \mathrm{f}'(x)\),</span><span class="inline-marks">[3]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Sketch on separate diagrams, the graphs of \(y = \frac{1}{\mathrm{f}(x)}\),</span><span class="inline-marks">[3]</span></div></li></ol></li></ol>
<p>showing clearly the main features of the graphs.</p>
<ol class="abc-list" start="2"><li><div class="list-item-content"><span class="list-item-text">Describe a sequence of transformations which transform the graph of \(y = \frac{x^2 + 1}{x}\) to the graph of \(y = \frac{2x^2 - 5x + 4}{x - 2}\).</span><span class="inline-marks">[3]</span></div></li></ol>

The diagram below shows a sketch of the graph of \(y = \mathrm{f}(x)\). The curve passes through the points with coordinates \((1, 0)\) and \((3, 0)\), and has turning points at \((1, 0)\) and \((4, 4)\). The asymptotes are \(x = 0\), \(x = 2\) and \(y = 2\).

Sketch on separate diagrams, the graphs of \(y = \mathrm{f}'(x)\),

Sketch on separate diagrams, the graphs of \(y = \frac{1}{\mathrm{f}(x)}\),

showing clearly the main features of the graphs.

Describe a sequence of transformations which transform the graph of \(y = \frac{x^2 + 1}{x}\) to the graph of \(y = \frac{2x^2 - 5x + 4}{x - 2}\).

Graphing Techniques

International Baccalaureate Higher Level Mathematics

2025 RI P1 Q5

2025 RI P1 Q5