OCR FP2 2007 June — Question 9

Exam BoardOCR
ModuleFP2 (Further Pure Mathematics 2)
Year2007
SessionJune
TopicPolynomial Division & Manipulation

9 It is given that the equation of a curve is $$y = \frac { x ^ { 2 } - 2 a x } { x - a }$$ where \(a\) is a positive constant.
  1. Find the equations of the asymptotes of the curve.
  2. Show that \(y\) takes all real values.
  3. Sketch the curve \(y = \frac { x ^ { 2 } - 2 a x } { x - a }\). \footnotetext{Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. OCR is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge. }