CAIE Further Paper 1 2023 November — Question 7

Exam BoardCAIE
ModuleFurther Paper 1 (Further Paper 1)
Year2023
SessionNovember
TopicCurve Sketching
TypeMultiple transformations including squared

7 The curve \(C\) has equation \(y = f ( x )\), where \(f ( x ) = \frac { x ^ { 2 } + 2 } { x ^ { 2 } - x - 2 }\).
  1. Find the equations of the asymptotes of \(C\).
  2. Find the coordinates of any stationary points on \(C\), giving your answers correct to 1 decimal place.
  3. Sketch \(C\), stating the coordinates of any intersections with the axes.
  4. Sketch the curve with equation \(\mathrm { y } = \frac { 1 } { \mathrm { f } ( \mathrm { x } ) }\).
  5. Find the set of values for which \(\frac { 1 } { \mathrm { f } ( x ) } < \mathrm { f } ( x )\).
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