OCR MEI FP1 2010 June — Question 7

Exam BoardOCR MEI
ModuleFP1 (Further Pure Mathematics 1)
Year2010
SessionJune
TopicPolynomial Division & Manipulation

7 Fig. 7 shows an incomplete sketch of \(y = \frac { ( 2 x - 1 ) ( x + 3 ) } { ( x - 3 ) ( x - 2 ) }\). \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e449d411-aaa9-4167-aa9c-c28d31446d52-3_786_1376_450_386} \captionsetup{labelformat=empty} \caption{Fig. 7}
\end{figure}
  1. Find the coordinates of the points where the curve cuts the axes.
  2. Write down the equations of the three asymptotes.
  3. Determine whether the curve approaches the horizontal asymptote from above or below for large positive values of \(x\), justifying your answer. Copy and complete the sketch.
  4. Solve the inequality \(\frac { ( 2 x - 1 ) ( x + 3 ) } { ( x - 3 ) ( x - 2 ) } < 2\).