OCR MEI FP1 2006 January — Question 7

Exam BoardOCR MEI
ModuleFP1 (Further Pure Mathematics 1)
Year2006
SessionJanuary
TopicPolynomial Division & Manipulation

7 A curve has equation \(y = \frac { 3 + x ^ { 2 } } { 4 - x ^ { 2 } }\).
  1. Show that \(y\) can never be zero.
  2. Write down the equations of the two vertical asymptotes and the one horizontal asymptote.
  3. Describe the behaviour of the curve for large positive and large negative values of \(x\), justifying your description.
  4. Sketch the curve.
  5. Solve the inequality \(\frac { 3 + x ^ { 2 } } { 4 - x ^ { 2 } } \leqslant - 2\).