AQA C3 2014 June — Question 4

Exam BoardAQA
ModuleC3 (Core Mathematics 3)
Year2014
SessionJune
TopicFunction Transformations
TypeMultiple separate transformations

4 The sketch shows part of the curve with equation \(y = \mathrm { f } ( x )\).
\includegraphics[max width=\textwidth, alt={}, center]{57412ec0-ad97-4418-8ba8-93f1f7d8aac1-08_536_1054_367_539}
  1. On Figure 2 below, sketch the curve with equation \(y = - | \mathrm { f } ( x ) |\).
  2. On Figure 3 on the page opposite, sketch the curve with equation \(y = \mathrm { f } ( | 2 x | )\).
    1. Describe a sequence of two geometrical transformations that maps the graph of \(y = \mathrm { f } ( x )\) onto the graph of \(y = \mathrm { f } ( 2 x + 2 )\).
    2. Find the coordinates of the image of the point \(P ( 4 , - 3 )\) under the sequence of transformations given in part (c)(i). \begin{figure}[h]
      \captionsetup{labelformat=empty} \caption{Figure 3} \includegraphics[alt={},max width=\textwidth]{57412ec0-ad97-4418-8ba8-93f1f7d8aac1-09_778_1032_424_529}
      \end{figure}