<p>The curve \(C\) has equation given by \(y = \frac{1 + 3x - 18x^2}{9x + 3}\).</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Without the use of a calculator, find the range of values that \(y\) can take.</span><span class="inline-marks">[4]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Sketch the graph of \(C\) indicating clearly its asymptotes and stationary points.</span><span class="inline-marks">[3]</span></div></li><li><div class="list-item-content"><span class="list-item-text">State a sequence of transformations that will transform the curve \(C\) to the curve with equation \(y = \frac{1 + 3(2x - 1) - 18(2x - 1)^2}{9(2x - 1) + 3}\).</span><span class="inline-marks">[2]</span></div></li></ol>

The curve \(C\) has equation given by \(y = \frac{1 + 3x - 18x^2}{9x + 3}\).

Without the use of a calculator, find the range of values that \(y\) can take.

Sketch the graph of \(C\) indicating clearly its asymptotes and stationary points.

State a sequence of transformations that will transform the curve \(C\) to the curve with equation \(y = \frac{1 + 3(2x - 1) - 18(2x - 1)^2}{9(2x - 1) + 3}\).

2025 ASRJC P1 Q5

2025 ASRJC P1 Q5