CAIE Further Paper 1 2022 June — Question 3

Exam BoardCAIE
ModuleFurther Paper 1 (Further Paper 1)
Year2022
SessionJune
TopicCurve Sketching
TypeRational functions with parameters

3 A curve \(C\) has equation \(\mathrm { y } = \frac { \mathrm { a } \mathrm { x } ^ { 2 } + \mathrm { x } - 1 } { \mathrm { x } - 1 }\), where \(a\) is a positive constant.
  1. Find the equations of the asymptotes of \(C\).
  2. Show that there is no point on \(C\) for which \(1 < \mathrm { y } < 1 + 4 \mathrm { a }\).
  3. Sketch C. You do not need to find the coordinates of the intersections with the axes.