<p>The diagram shows the graph of \(y = \mathrm{f}(x)\) with asymptotes \(x = 0\) and \(y = 2x - 1\). The graph has a turning point at \(\left(2, \frac{21}{4}\right)\) and it cuts the \(x\)-axis at \(x = a\) where&nbsp;\(a &lt; 0\).</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/1779465259176-jks9ys3gxbb.png" style="max-width: min(300px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="i-list"><li><div class="list-item-paragraph">Sketch the graph of \(y = \mathrm{f}'(x)\), stating the equations of any asymptotes and the coordinates of any turning points and points of intersection with the axes.<span class="inline-marks">[3]</span></div></li><li><div class="list-item-paragraph">The curve \(y = \mathrm{f}(x)\) undergoes the transformations \(A\), \(B\) and \(C\) in succession.<br><br>\(\qquad A\): A translation of \(2\) units in the negative \(x\)-direction.<br>\(\qquad B\): A stretch parallel to the \(y\)-axis with scale factor \(2\).<br>\(\qquad C\): A translation of \(1\) unit in the positive \(y\)-direction.<br><br>Find the equations of the asymptotes of the resulting curve.<span class="inline-marks">[3]</span></div></li></ol>

The diagram shows the graph of \(y = \mathrm{f}(x)\) with asymptotes \(x = 0\) and \(y = 2x - 1\). The graph has a turning point at \(\left(2, \frac{21}{4}\right)\) and it cuts the \(x\)-axis at \(x = a\) where \(a < 0\).

Sketch the graph of \(y = \mathrm{f}'(x)\), stating the equations of any asymptotes and the coordinates of any turning points and points of intersection with the axes.

The curve \(y = \mathrm{f}(x)\) undergoes the transformations \(A\), \(B\) and \(C\) in succession.

\(\qquad A\): A translation of \(2\) units in the negative \(x\)-direction.
\(\qquad B\): A stretch parallel to the \(y\)-axis with scale factor \(2\).
\(\qquad C\): A translation of \(1\) unit in the positive \(y\)-direction.

Find the equations of the asymptotes of the resulting curve.

2024 MI PRU2 P1 Q2

2024 MI PRU2 P1 Q2