CAIE Further Paper 1 2022 June — Question 5

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

5 The curve \(C\) has equation \(y = \frac { 2 x ^ { 2 } - x - 1 } { x ^ { 2 } + x + 1 }\).
  1. Show that \(C\) has no vertical asymptotes and state the equation of the horizontal asymptote of \(C\).
  2. Find the coordinates of the stationary points on \(C\).
  3. Sketch \(C\), stating the coordinates of the intersections with the axes.
  4. Sketch the curve with equation \(y = \left| \frac { 2 x ^ { 2 } - x - 1 } { x ^ { 2 } + x + 1 } \right|\) and state the set of values of \(k\) for which \(\left| \frac { 2 x ^ { 2 } - x - 1 } { x ^ { 2 } + x + 1 } \right| = k\) has 4 distinct real solutions.