Edexcel C1 2011 January — Question 5

Exam BoardEdexcel
ModuleC1 (Core Mathematics 1)
Year2011
SessionJanuary
TopicFunction Transformations
TypeComposite transformation sketch

5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{95e11fd7-765c-477d-800b-7574bc1af81f-06_640_1063_322_438} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows a sketch of the curve with equation \(y = \mathrm { f } ( x )\) where $$\mathrm { f } ( x ) = \frac { x } { x - 2 } , \quad x \neq 2$$ The curve passes through the origin and has two asymptotes, with equations \(y = 1\) and \(x = 2\), as shown in Figure 1.
  1. In the space below, sketch the curve with equation \(y = \mathrm { f } ( x - 1 )\) and state the equations of the asymptotes of this curve.
  2. Find the coordinates of the points where the curve with equation \(y = \mathrm { f } ( x - 1 )\) crosses the coordinate axes.