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.

9 questions

OCR MEI C2 Q8
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
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 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
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. \(y = \frac { 1 } { 4 } \mathrm { f } ( x )\)
OCR MEI C2 2010 January Q5
5 \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{053009a4-e88f-4711-ad97-cebb1740744b-2_547_991_1340_577} \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. \(y = \frac { 1 } { 4 } \mathrm { f } ( x )\)
OCR MEI C2 2013 June Q8
8 Fig. 8 shows the graph of \(y = \mathrm { g } ( x )\). \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ee79022b-b9a6-4076-8db7-67b9788ac28a-4_800_1402_1382_328} \captionsetup{labelformat=empty} \caption{Fig. 8}
\end{figure} Draw the graph of
  1. \(y = \mathrm { g } ( 2 x )\),
  2. \(y = 3 \mathrm {~g} ( x )\). Section B (36 marks)
Edexcel C12 2018 January Q8
  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.
OCR Stats 1 2018 December Q3
3
\includegraphics[max width=\textwidth, alt={}, center]{166bcf11-c812-4077-91c8-916b093cbbd0-05_796_1653_260_205} The diagram shows the graph of \(y = \mathrm { g } ( x )\).
In the printed answer booklet, using the same scale as in this diagram, sketch the curves
  1. \(\quad y = \frac { 3 } { 2 } \mathrm {~g} ( x )\),
  2. \(y = \mathrm { g } \left( \frac { 1 } { 2 } x \right)\).
OCR MEI C2 2010 June Q4
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]{e5ac28f3-d61a-4b40-8b47-28c930761a28-2_789_887_1427_628} \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.