CAIE FP1 2012 November — Question 7

Exam BoardCAIE
ModuleFP1 (Further Pure Mathematics 1)
Year2012
SessionNovember
TopicCurve Sketching
TypeRational functions with parameters

7 The curve \(C\) has equation $$y = \lambda x + \frac { x } { x - 2 }$$ where \(\lambda\) is a non-zero constant. Find the equations of the asymptotes of \(C\). Show that \(C\) has no turning points if \(\lambda < 0\). Sketch \(C\) in the case \(\lambda = - 1\), stating the coordinates of the intersections with the axes.