CAIE Further Paper 1 2022 November — Question 7

Exam BoardCAIE
ModuleFurther Paper 1 (Further Paper 1)
Year2022
SessionNovember
TopicCurve Sketching
TypeSolve |f(x)| > k using sketch

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