OCR MEI C1 2008 January — Question 10

Exam BoardOCR MEI
ModuleC1 (Core Mathematics 1)
Year2008
SessionJanuary
TopicFunction Transformations
TypeTransformation of specific function type

10
  1. \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{450c1c3a-9290-4afa-a051-112b60cf19c0-3_753_775_360_726} \captionsetup{labelformat=empty} \caption{Fig. 10}
    \end{figure} Fig. 10 shows a sketch of the graph of \(y = \frac { 1 } { x }\).
    Sketch the graph of \(y = \frac { 1 } { x - 2 }\), showing clearly the coordinates of any points where it crosses the axes.
  2. Find the value of \(x\) for which \(\frac { 1 } { x - 2 } = 5\).
  3. Find the \(x\)-coordinates of the points of intersection of the graphs of \(y = x\) and \(y = \frac { 1 } { x - 2 }\). Give your answers in the form \(a \pm \sqrt { b }\). Show the position of these points on your graph in part (i).