<ol class="abc-list"><li><div class="list-item-paragraph">Describe a sequence of \(2\) transformations that transforms the curve \(C\) with equation \(\frac{x^2}{9} + y^2 = 1\) onto the curve \(D\) with equation \((x - 2)^2 + y^2 = 1\).<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">The diagram shows the curve with equation \(y = \mathrm{f}(x)\). The curve passes through the origin and the point \((2, 0)\) and has a minimum point at \((3, -4)\). The asymptotes of the curve are the lines \(x = 1\), \(y = 0\) and \(y = 2\).</div><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1779464100837-ul9e1oubgg8.png" alt="List item image" class="aligncenter custom-width" style="max-width: min(350px, 100%); height: auto;" /></div><div class="list-item-paragraph">Sketch the graph of \(y = \frac{1}{\mathrm{f}(x)}\), indicating the equations of any asymptotes and the coordinates of any points where it crosses the axes and of any turning points, where applicable.<span class="inline-marks">[3]</span></div></li><li><div class="list-item-paragraph">The graph of \(y = \mathrm{g}(x)\) is a semi-circle with its centre at the point \((a, 0)\), where&nbsp;\(a &lt; 0\). The diagram shows the graph of \(y = \mathrm{g}(|x|)\), which intersects the axes at the points \((-b, 0)\), \((b, 0)\) and \((0, c)\), where&nbsp;\(a \neq -b\).<span class="inline-marks">[3]</span></div><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1779464201449-pjwnanel4gn.png" alt="List item image" class="aligncenter custom-width" style="max-width: min(250px, 100%); height: auto;" /></div><div class="list-item-paragraph">Sketch the graph of \(y = \mathrm{g}(x)\), labelling the coordinates of the centre and the radius of the semi-circle, in terms of \(a\) and/or \(b\).</div></li></ol>

Describe a sequence of \(2\) transformations that transforms the curve \(C\) with equation \(\frac{x^2}{9} + y^2 = 1\) onto the curve \(D\) with equation \((x - 2)^2 + y^2 = 1\).

The diagram shows the curve with equation \(y = \mathrm{f}(x)\). The curve passes through the origin and the point \((2, 0)\) and has a minimum point at \((3, -4)\). The asymptotes of the curve are the lines \(x = 1\), \(y = 0\) and \(y = 2\).

Sketch the graph of \(y = \frac{1}{\mathrm{f}(x)}\), indicating the equations of any asymptotes and the coordinates of any points where it crosses the axes and of any turning points, where applicable.

The graph of \(y = \mathrm{g}(x)\) is a semi-circle with its centre at the point \((a, 0)\), where \(a < 0\). The diagram shows the graph of \(y = \mathrm{g}(|x|)\), which intersects the axes at the points \((-b, 0)\), \((b, 0)\) and \((0, c)\), where \(a \neq -b\).

Sketch the graph of \(y = \mathrm{g}(x)\), labelling the coordinates of the centre and the radius of the semi-circle, in terms of \(a\) and/or \(b\).

2024 MI PRU1 Q5

2024 MI PRU1 Q5