9231 P12 - Jun 2025 - Q07 - 15 marks
4113
The curve \(C\) has equation \(y = \frac{2x^2 - 5x}{2x^2 - 7x - 4}\).
- Find the equations of the asymptotes of \(C\).
- Find the coordinates of any stationary points on \(C\).
- Sketch \(C\), stating the coordinates of the intersections with the axes.
- Sketch the curve with equation \(y = \left| \frac{2x^2 - 5x}{2x^2 - 7x - 4} \right|\).
- Find in exact form the set of values of \(x\) for which \(\left| \frac{2x^2 - 5x}{2x^2 - 7x - 4} \right| < \frac{1}{9}\).
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