Combined transformation sketches

Questions asking students to sketch a composition of multiple transformations applied together (e.g., -4f(x+3), f(|x|+1)) requiring students to apply transformations in sequence.

3 questions · Standard +0.6

1.02w Graph transformations: simple transformations of f(x)1.02x Combinations of transformations: multiple transformations
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Edexcel C3 2012 January Q2
6 marks Standard +0.3
[diagram]
Figure 1 shows the graph of equation \(y = \mathrm { f } ( x )\).
The points \(P ( - 3,0 )\) and \(Q ( 2 , - 4 )\) are stationary points on the graph.
Sketch, on separate diagrams, the graphs of
  1. \(y = 3 \mathrm { f } ( x + 2 )\)
  2. \(y = | \mathrm { f } ( x ) |\) On each diagram, show the coordinates of any stationary points.
OCR C3 2011 January Q2
4 marks Moderate -0.3
2 \includegraphics[max width=\textwidth, alt={}, center]{774bb427-5392-45d3-8e4e-47d08fb8a792-02_538_1061_388_541} The diagram shows the curve with equation \(y = \mathrm { f } ( x )\). It is given that \(\mathrm { f } ( - 7 ) = 0\) and that there are stationary points at \(( - 2 , - 6 )\) and \(( 0,0 )\). Sketch the curve with equation \(y = - 4 \mathrm { f } ( x + 3 )\), indicating the coordinates of the stationary points.
Edexcel AEA 2005 June Q6
19 marks Challenging +1.8
  1. Find the coordinates of the points \(P , Q\) and \(R\).
  2. Sketch, on separate diagrams, the graphs of
    1. \(y = \mathrm { f } ( 2 x )\),
    2. \(y = \mathrm { f } ( | x | + 1 )\),
      indicating on each sketch the coordinates of any maximum points and the intersections with the \(x\)-axis.
      (6) \begin{figure}[h]
      \captionsetup{labelformat=empty} \caption{Figure 2} \includegraphics[alt={},max width=\textwidth]{f9d3e02c-cef2-435b-9cda-76c43fcac575-5_1015_1464_232_337}
      \end{figure} Figure 2 shows a sketch of part of the curve \(C\), with equation \(y = \mathrm { f } ( x - v ) + w\), where \(v\) and \(w\) are constants. The \(x\)-axis is a tangent to \(C\) at the minimum point \(T\), and \(C\) intersects the \(y\)-axis at \(S\). The line joining \(S\) to the maximum point \(U\) is parallel to the \(x\)-axis.
  3. Find the value of \(v\) and the value of \(w\) and hence find the roots of the equation $$f ( x - v ) + w = 0$$