<ol class="abc-list"><li><div class="list-item-paragraph">The diagram below shows the graph of \(y = \mathrm{f}(x)\). The curve passes through the points \(A(-a,0)\) and \(B(0,-a)\) and has a minimum point at \(C(2a,-2a)\), where&nbsp;\(a &gt; 0\). The lines \(x = -2a\) and \(y = -a\) are asymptotes of the curve.</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/1779453402163-dw91vlxqcgf.png" alt="List item image" class="aligncenter custom-width" style="max-width: min(350px, 100%); height: auto;" /></div><div class="list-item-paragraph">On separate diagrams, sketch the graph of </div><ol class="i-list"><li><div class="list-item-paragraph">\(y = \mathrm{f}(x-a) + a\),<span class="inline-marks">[3]</span></div></li><li><div class="list-item-paragraph">\(y = \frac{1}{\mathrm{f}(x)}\),<span class="inline-marks">[3]</span></div></li></ol></li><li><div class="list-item-paragraph">The curve whose equation is \(y = \sin x\), undergoes in succession, the following transformations:<br><br>\(\mathbf{A}\): A translation by \(\pi\) units in the negative \(x\)-direction.<br>\(\mathbf{B}\): A scaling parallel to the \(x\)-axis by a factor of \(3\).<br>\(\mathbf{C}\): A translation by \(2\) units in the positive \(y\)-direction.<br><br>Find the equation of the resulting curve.<span class="inline-marks">[3]</span></div></li></ol>

The diagram below shows the graph of \(y = \mathrm{f}(x)\). The curve passes through the points \(A(-a,0)\) and \(B(0,-a)\) and has a minimum point at \(C(2a,-2a)\), where \(a > 0\). The lines \(x = -2a\) and \(y = -a\) are asymptotes of the curve.

On separate diagrams, sketch the graph of 

The curve whose equation is \(y = \sin x\), undergoes in succession, the following transformations:

\(\mathbf{A}\): A translation by \(\pi\) units in the negative \(x\)-direction.
\(\mathbf{B}\): A scaling parallel to the \(x\)-axis by a factor of \(3\).
\(\mathbf{C}\): A translation by \(2\) units in the positive \(y\)-direction.

Find the equation of the resulting curve.

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