<p>The diagram below shows the graph of \(y = \mathrm{f}(2x)\). The graph has a turning point at \((2, 0)\), and asymptotes with equations \(x = 0\) and \(y = k\).</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/1781078497751-lxlb0yqkjyq.png" style="max-width: min(400px, 100%); height: auto; display: block;" alt="Diagram as shown in the question" class="aligncenter custom-width" /></figure></div>
<ol class="abc-list"><li data-list-item-id="item-a"><div class="list-item-paragraph">State a single transformation that will transform the graph of \(y = \mathrm{f}(2x)\) onto the graph of \(y = \mathrm{f}(2x + 4)\). Hence sketch the graph of \(y = \mathrm{f}(2x + 4)\).<span class="inline-marks">[3]</span></div></li></ol>
<p>On separate clearly labelled diagrams, sketch the graphs of</p>
<ol class="abc-list" start="2"><li data-list-item-id="item-b"><div class="list-item-paragraph">\(y = \frac{1}{\mathrm{f}(2x)}\)<span class="inline-marks">[3]</span></div></li><li data-list-item-id="item-c"><div class="list-item-paragraph">\(y = -\mathrm{f}(|x|)\)<span class="inline-marks">[3]</span></div></li></ol>

The diagram below shows the graph of \(y = \mathrm{f}(2x)\). The graph has a turning point at \((2, 0)\), and asymptotes with equations \(x = 0\) and \(y = k\).

State a single transformation that will transform the graph of \(y = \mathrm{f}(2x)\) onto the graph of \(y = \mathrm{f}(2x + 4)\). Hence sketch the graph of \(y = \mathrm{f}(2x + 4)\).

On separate clearly labelled diagrams, sketch the graphs of

Functions and Graphs

Functions and Graphs