OCR MEI FP1 2016 June — Question 8

Exam BoardOCR MEI
ModuleFP1 (Further Pure Mathematics 1)
Year2016
SessionJune
TopicPolynomial Division & Manipulation

8 A curve has equation \(y = \frac { 3 x ^ { 2 } - 9 } { x ^ { 2 } + 3 x - 4 }\).
  1. Find the equations of the two vertical asymptotes and the one horizontal asymptote of this curve.
  2. State, with justification, how the curve approaches the horizontal asymptote for large positive and large negative values of \(x\).
  3. Sketch the curve.
  4. Solve the inequality \(\frac { 3 x ^ { 2 } - 9 } { x ^ { 2 } + 3 x - 4 } \geqslant 0\).