CAIE FP1 2018 June — Question 6

Exam BoardCAIE
ModuleFP1 (Further Pure Mathematics 1)
Year2018
SessionJune
TopicPolynomial Division & Manipulation

6 The curve \(C\) has equation $$y = \frac { x ^ { 2 } + b } { x + b }$$ where \(b\) is a positive constant.
  1. Find the equations of the asymptotes of \(C\).
  2. Show that \(C\) does not intersect the \(x\)-axis.
  3. Justifying your answer, find the number of stationary points on \(C\).
  4. Sketch C. Your sketch should indicate the coordinates of any points of intersection with the \(y\)-axis. You do not need to find the coordinates of any stationary points.