OCR MEI FP1 — Question 7

Exam BoardOCR MEI
ModuleFP1 (Further Pure Mathematics 1)
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TopicCurve Sketching
7 A curve has equation \(y = \frac { ( 2 x - 3 ) ( x + 1 ) } { ( x + 4 ) ( x - 2 ) }\).
  1. Write down the values of \(x\) for which \(y = 0\).
  2. Write down the equations of the three asymptotes.
  3. Determine whether the curve approaches the horizontal asymptote from above or from below for
    (A) large positive values of \(x\),
    (B) large negative values of \(x\).
  4. Sketch the curve.
  5. Solve the inequality \(\frac { ( 2 x - 3 ) ( x + 1 ) } { ( x + 4 ) ( x - 2 ) } \leqslant 2\).
7 A curve has equation $y = \frac { ( 2 x - 3 ) ( x + 1 ) } { ( x + 4 ) ( x - 2 ) }$.\\
(i) Write down the values of $x$ for which $y = 0$.\\
(ii) Write down the equations of the three asymptotes.\\
(iii) Determine whether the curve approaches the horizontal asymptote from above or from below for\\
(A) large positive values of $x$,\\
(B) large negative values of $x$.\\
(iv) Sketch the curve.\\
(v) Solve the inequality $\frac { ( 2 x - 3 ) ( x + 1 ) } { ( x + 4 ) ( x - 2 ) } \leqslant 2$.

\hfill \mbox{\textit{OCR MEI FP1  Q7}}
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