Identify transformation from two graphs

Questions that show two graphs (or multiple graphs) and ask students to identify or state the transformation that maps one to the other, or to state the equation of a transformed graph.

5 questions · Moderate -1.0

1.02w Graph transformations: simple transformations of f(x)
Sort by: Default | Easiest first | Hardest first
OCR MEI C2 2007 June Q3
4 marks Easy -1.2
3 \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{2bdf241f-4538-4227-ba00-fe843d1b3aca-2_830_1393_959_334} \captionsetup{labelformat=empty} \caption{Fig. 3}
\end{figure} Fig. 3 shows sketches of three graphs, A, B and C. The equation of graph A is \(y = \mathrm { f } ( x )\). State the equation of
  1. graph B ,
  2. graph C.
OCR MEI C2 Q6
4 marks Moderate -0.8
6 \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{669be128-491c-4152-8f3a-e37a34dd9383-3_819_1370_271_383} \captionsetup{labelformat=empty} \caption{Fig. 3}
\end{figure} Fig. 3 shows sketches of three graphs, A, B and C. The equation of graph A is \(y = \mathrm { f } ( x )\). State the equation of
  1. graph B ,
  2. graph C .
OCR MEI C2 Q9
3 marks Moderate -0.8
9 Figs. 5.1 and 5.2 show the graph of \(y = \sin x\) for values of \(x\) from \(0 ^ { \circ }\) to \(360 ^ { \circ }\) and two transformations of this graph. State the equation of each graph after it has been transformed.
  1. \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{669be128-491c-4152-8f3a-e37a34dd9383-4_511_941_828_586} \captionsetup{labelformat=empty} \caption{Fig. 5.1}
    \end{figure}
  2. \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{669be128-491c-4152-8f3a-e37a34dd9383-4_517_937_1508_584} \captionsetup{labelformat=empty} \caption{Fig. 5.2}
    \end{figure}
OCR C1 2010 January Q7
5 marks Easy -1.3
7 \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{918d83c3-1608-4482-9d3d-8af05e65f353-3_618_606_255_397} \captionsetup{labelformat=empty} \caption{Fig. 1}
\end{figure} \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{918d83c3-1608-4482-9d3d-8af05e65f353-3_622_622_251_1128} \captionsetup{labelformat=empty} \caption{Fig. 2}
\end{figure} \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{918d83c3-1608-4482-9d3d-8af05e65f353-3_620_613_986_395} \captionsetup{labelformat=empty} \caption{Fig. 3}
\end{figure} \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{918d83c3-1608-4482-9d3d-8af05e65f353-3_620_611_986_1128} \captionsetup{labelformat=empty} \caption{Fig. 4}
\end{figure}
  1. Each diagram shows a quadratic curve. State which diagram corresponds to the curve
    1. \(y = ( 3 - x ) ^ { 2 }\),
    2. \(y = x ^ { 2 } + 9\),
    3. \(y = ( 3 - x ) ( x + 3 )\).
    4. Give the equation of the curve which does not correspond to any of the equations in part (i).
OCR MEI C2 2012 January Q5
3 marks Moderate -0.8
5 Figs. 5.1 and 5.2 show the graph of \(y = \sin x\) for values of \(x\) from \(0 ^ { \circ }\) to \(360 ^ { \circ }\) and two transformations of this graph. State the equation of each graph after it has been transformed.
  1. \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{ba9f2fd1-7a36-4749-86ec-40c93d23a84b-2_506_926_1324_571} \captionsetup{labelformat=empty} \caption{Fig. 5.1}
    \end{figure}
  2. \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{ba9f2fd1-7a36-4749-86ec-40c93d23a84b-2_513_936_2003_561} \captionsetup{labelformat=empty} \caption{Fig. 5.2}
    \end{figure}