Question 6 - A-Level Maths

Exam Board	OCR MEI
Module	C1 (Core Mathematics 1)
Topic	Function Transformations
Type	Single transformation sketch

\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{9106e6b2-0b36-4ebf-ace3-a30570df73d3-2_754_780_317_763} \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.
Find the value of \(x\) for which \(\frac { 1 } { x - 2 } = 5\).
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).