9231 P11 - Jun 2025 - Q07 - 15 marks
4121
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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