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2025 ASRJC P1 Q5

2025 ASRJC P1 Q5

9 marks

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

  1. Without the use of a calculator, find the range of values that \(y\) can take.[4]
  2. Sketch the graph of \(C\) indicating clearly its asymptotes and stationary points.[3]
  3. State a sequence of transformations that will transform the curve \(C\) to the curve with equation \(y = \frac{1 + 3(2x - 1) - 18(2x - 1)^2}{9(2x - 1) + 3}\).[2]

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Answer:(a) \(y\le\dfrac13\) or \(y\ge3\) (b) asymptotes \(x=-\dfrac13\) and \(y=-2x+1\), stationary points \(\left(-\dfrac23,3\right)\) and \(\left(0,\dfrac13\right)\) (c) translate \(1\) unit right, then scale by factor \(\dfrac12\) parallel to the \(x\)-axis

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