CAIE Further Paper 1 2024 June — Question 6 2 marks

Exam BoardCAIE
ModuleFurther Paper 1 (Further Paper 1)
Year2024
SessionJune
Marks2
TopicCurve Sketching
TypeSimple rational function analysis

6 The curve \(C\) has equation \(y = \frac { x + 1 } { x ^ { 2 } + 3 }\).
  1. Show that \(C\) has no vertical asymptotes and state the equation of the horizontal asymptote. [2]
  2. Find the coordinates of any stationary points on \(C\).
    \includegraphics[max width=\textwidth, alt={}, center]{7eb2abb1-68f4-4cc8-8314-f436906d6c4e-12_2715_35_144_2012}
    \includegraphics[max width=\textwidth, alt={}, center]{7eb2abb1-68f4-4cc8-8314-f436906d6c4e-13_2718_33_141_23}
  3. Sketch \(C\), stating the coordinates of the intersections with the axes.
  4. Sketch \(y ^ { 2 } = \frac { x + 1 } { x ^ { 2 } + 3 }\), stating the coordinates of the stationary points and the intersections with the axes.