Edexcel C3 2010 January — Question 6

Exam BoardEdexcel
ModuleC3 (Core Mathematics 3)
Year2010
SessionJanuary
TopicFunction Transformations
TypeMultiple separate transformations

6. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{b2f133cc-1723-4512-a351-c319daf80fca-07_380_574_269_722} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows a sketch of the graph of \(y = \mathrm { f } ( x )\).
The graph intersects the \(y\)-axis at the point \(( 0,1 )\) and the point \(A ( 2,3 )\) is the maximum turning point. Sketch, on separate axes, the graphs of
  1. \(y = \mathrm { f } ( - x ) + 1\),
  2. \(y = \mathrm { f } ( x + 2 ) + 3\),
  3. \(y = 2 \mathrm { f } ( 2 x )\). On each sketch, show the coordinates of the point at which your graph intersects the \(y\)-axis and the coordinates of the point to which \(A\) is transformed.