Two stretches from same function

Questions asking to sketch both y = af(x) and y = f(bx) starting from the same given function f(x), requiring direct application of vertical and horizontal stretch transformations.

7 questions · Moderate -0.8

1.02w Graph transformations: simple transformations of f(x)
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Edexcel C1 2008 January Q6
7 marks Moderate -0.8
6. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ba0ee180-4c22-49f7-8a8e-a7268828b067-07_693_676_370_632} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows a sketch of the curve with equation \(y = \mathrm { f } ( x )\). The curve crosses the \(x\)-axis at the points \(( 1,0 )\) and \(( 4,0 )\). The maximum point on the curve is \(( 2,5 )\).
In separate diagrams sketch the curves with the following equations.
On each diagram show clearly the coordinates of the maximum point and of each point at which the curve crosses the \(x\)-axis.
  1. \(y = 2 \mathrm { f } ( x )\),
  2. \(y = \mathrm { f } ( - x )\). The maximum point on the curve with equation \(y = \mathrm { f } ( x + a )\) is on the \(y\)-axis.
  3. Write down the value of the constant \(a\).
Edexcel C1 2010 June Q6
7 marks Moderate -0.8
6. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{65d61b2c-2e47-402e-b08f-2d46bb00c188-08_568_942_269_498} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows a sketch of the curve with equation \(y = \mathrm { f } ( x )\). The curve has a maximum point \(A\) at \(( - 2,3 )\) and a minimum point \(B\) at \(( 3 , - 5 )\). On separate diagrams sketch the curve with equation
  1. \(y = \mathrm { f } ( x + 3 )\)
  2. \(y = 2 \mathrm { f } ( x )\) On each diagram show clearly the coordinates of the maximum and minimum points.
    The graph of \(y = \mathrm { f } ( x ) + a\) has a minimum at (3, 0), where \(a\) is a constant.
  3. Write down the value of \(a\).
OCR MEI C2 Q8
4 marks Easy -1.8
8 Draw two sketches of the graph of \(y = \sin x\) in the range \(0 ^ { \circ } \leq x \leq 360 ^ { \circ }\).
  1. On the first sketch, draw also a sketch of \(y = \sin ( 2 x )\).
  2. On the second sketch, draw also a sketch of \(y = 2 \sin x\).
OCR MEI C2 Q2
4 marks Moderate -0.8
2 Fig. 8 shows the graph of \(y = \mathrm { g } ( x )\). \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{669be128-491c-4152-8f3a-e37a34dd9383-1_800_1401_781_385} \captionsetup{labelformat=empty} \caption{Fig. 8}
\end{figure} Draw the graph of
  1. \(y = \mathrm { g } ( 2 x )\),
  2. \(y = 3 \mathrm {~g} ( x )\).
OCR MEI C2 Q4
4 marks Moderate -0.3
4 In this question, \(\mathrm { f } ( x ) = x ^ { 2 } - 5 x\). Fig. 4 shows a sketch of the graph of \(y = \mathrm { f } ( x )\). \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{669be128-491c-4152-8f3a-e37a34dd9383-2_795_898_824_654} \captionsetup{labelformat=empty} \caption{Fig. 4}
\end{figure} On separate diagrams, sketch the curves \(y = \mathrm { f } ( 2 x )\) and \(y = 3 \mathrm { f } ( x )\), labelling the coordinates of their intersections with the axes and their turning points.
OCR MEI C2 Q11
4 marks Moderate -0.8
11 \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{669be128-491c-4152-8f3a-e37a34dd9383-5_546_989_828_596} \captionsetup{labelformat=empty} \caption{Fig. 5}
\end{figure} Fig. 5 shows a sketch of the graph of \(y = \mathrm { f } ( x )\). On separate diagrams, sketch the graphs of the following, showing clearly the coordinates of the points corresponding to \(\mathrm { P } , \mathrm { Q }\) and R .
  1. \(y = \mathrm { f } ( 2 x )\)
  2. \(y = \frac { 1 } { 4 } \mathrm { f } ( x )\)
Edexcel C12 2018 January Q8
6 marks Moderate -0.5
  1. \(y = \mathrm { f } ( - x )\)
  2. \(y = \mathrm { f } ( 2 x )\) On each diagram, show clearly the coordinates of any points of intersection of the curve with the two coordinate axes and the coordinates of the stationary points.