AQA C3 2012 June — Question 7

Exam BoardAQA
ModuleC3 (Core Mathematics 3)
Year2012
SessionJune
TopicFunction Transformations
TypeMultiple separate transformations

7 The sketch shows part of the curve with equation \(y = \mathrm { f } ( x )\).
\includegraphics[max width=\textwidth, alt={}, center]{d3c66c34-b09c-4223-8383-cf0a68419bf9-5_632_1029_712_541}
  1. On Figure 2 on page 6, sketch the curve with equation \(y = | \mathrm { f } ( x ) |\).
  2. On Figure 3 on page 6, sketch the curve with equation \(y = \mathrm { f } ( | x | )\).
  3. Describe a sequence of two geometrical transformations that maps the graph of \(y = \mathrm { f } ( x )\) onto the graph of \(y = \frac { 1 } { 2 } \mathrm { f } ( x + 1 )\).
  4. The maximum point of the curve with equation \(y = \mathrm { f } ( x )\) has coordinates \(( - 1,10 )\). Find the coordinates of the maximum point of the curve with equation \(y = \frac { 1 } { 2 } \mathrm { f } ( x + 1 )\).
    (2 marks)
  5. \begin{figure}[h]
    \captionsetup{labelformat=empty} \caption{Figure 2} \includegraphics[alt={},max width=\textwidth]{d3c66c34-b09c-4223-8383-cf0a68419bf9-6_785_1022_358_548}
    \end{figure}
  6. \begin{figure}[h]
    \captionsetup{labelformat=empty} \caption{Figure 3} \includegraphics[alt={},max width=\textwidth]{d3c66c34-b09c-4223-8383-cf0a68419bf9-6_776_1022_1395_548}
    \end{figure}