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9231 P12 - Nov 2022 - Q07 - 15 marks
4259

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

  1. Find the equations of the asymptotes of C.
  2. Find the exact coordinates of the stationary points on C.
  3. Sketch C, stating the coordinates of any intersections with the axes.
  4. Sketch the curve with equation \(y = \left| \frac{x^2 - x}{x + 1} \right|\) and find in exact form the set of values of \(x\) for which \(\left| \frac{x^2 - x}{x + 1} \right| < 6\).
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