CAIE Further Paper 1 2021 November — Question 6 1 marks

Exam BoardCAIE
ModuleFurther Paper 1 (Further Paper 1)
Year2021
SessionNovember
Marks1
TopicCurve Sketching
TypeSolve |f(x)| > k using sketch

6 The curve \(C\) has equation \(\mathrm { y } = \frac { \mathrm { x } ^ { 2 } } { \mathrm { x } - 3 }\).
  1. Find the equations of the asymptotes of \(C\).
  2. Show that there is no point on \(C\) for which \(0 < y < 12\).
  3. Sketch C.
    1. Sketch the graphs of \(y = \left| \frac { x ^ { 2 } } { x - 3 } \right|\) and \(y = | x | - 3\) on a single diagram, stating the coordinates of the intersections with the axes.
    2. Use your sketch to find the set of values of \(c\) for which \(\left| \frac { x ^ { 2 } } { x - 3 } \right| \leqslant | x | + c\) has no solution. [1]