<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">The graph of \(y=\mathrm{f}(x)\) has turning points at \(A(-a, 0)\), \(B(a, b)\) and \(C(c, -b)\) and intersects the \(x\)-axis at the points \(D(d, 0)\) and \(E(e, 0)\). The graph of \(y=\mathrm{f}(x)\) is as shown in the diagram below.</span><span class="inline-marks">[3]</span></div></li></ol>
<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/1769223141925-ir1uwhrzoth.png" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<p>Sketch the graph of \(y=\mathrm{f}(a-x)\), labelling the coordinates of the corresponding points of \(A\), \(B\), \(C\), \(D\), and \(E\) clearly.<span class="inline-marks">[3]</span></p>
<ol class="abc-list" start="2"><li><div class="list-item-content"><span class="list-item-text">The graph of \(y=\mathrm{g}(x)\) has asymptotes \(y=0\), \(y=-m\) and \(x=-n\), and intersects the \(y\)-axis at \(P(0, p)\), where \(p &lt; m\). The graph of \(y=\mathrm{g}(x)\) is as shown in the diagram below.</span></div></li></ol>
<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/1769223158996-vh24fdfkh2.png" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<p>Sketch on separate diagrams the graphs of</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">\(y=|\mathrm{g}(x)|\) and</span><span class="inline-marks">[3]</span></div></li><li><div class="list-item-content"><span class="list-item-text">\(y=\mathrm{g}(|x|)\),</span><span class="inline-marks">[2]</span></div></li></ol>
<p>labelling clearly the asymptote(s) and coordinates of \(P\) on each graph.</p>

The graph of \(y=\mathrm{f}(x)\) has turning points at \(A(-a, 0)\), \(B(a, b)\) and \(C(c, -b)\) and intersects the \(x\)-axis at the points \(D(d, 0)\) and \(E(e, 0)\). The graph of \(y=\mathrm{f}(x)\) is as shown in the diagram below.

Sketch the graph of \(y=\mathrm{f}(a-x)\), labelling the coordinates of the corresponding points of \(A\), \(B\), \(C\), \(D\), and \(E\) clearly.

The graph of \(y=\mathrm{g}(x)\) has asymptotes \(y=0\), \(y=-m\) and \(x=-n\), and intersects the \(y\)-axis at \(P(0, p)\), where \(p < m\). The graph of \(y=\mathrm{g}(x)\) is as shown in the diagram below.

Sketch on separate diagrams the graphs of

labelling clearly the asymptote(s) and coordinates of \(P\) on each graph.

Graphing Techniques

International Baccalaureate Higher Level Mathematics

2025 NYJC P1 Q4

2025 NYJC P1 Q4