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.

6 questions

OCR MEI C1 2006 January Q2
2 \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{7a4a7ff2-d196-4645-96f1-9c994caab0a2-2_526_524_541_767} \captionsetup{labelformat=empty} \caption{Fig. 2}
\end{figure} Fig. 2 shows graphs \(A\) and \(B\).
  1. State the transformation which maps graph \(A\) onto graph \(B\).
  2. The equation of graph \(A\) is \(y = \mathrm { f } ( x )\). Which one of the following is the equation of graph \(B\) ? $$\begin{array} { l l l l } y = \mathrm { f } ( x ) + 2 & y = \mathrm { f } ( x ) - 2 & y = \mathrm { f } ( x + 2 ) & y = \mathrm { f } ( x - 2 )
    y = 2 \mathrm { f } ( x ) & y = \mathrm { f } ( x + 3 ) & y = \mathrm { f } ( x - 3 ) & y = 3 \mathrm { f } ( x ) \end{array}$$
OCR MEI C2 2007 June Q3
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
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
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
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
    (a) \(y = ( 3 - x ) ^ { 2 }\),
    (b) \(y = x ^ { 2 } + 9\),
    (c) \(y = ( 3 - x ) ( x + 3 )\).
  2. Give the equation of the curve which does not correspond to any of the equations in part (i).
OCR MEI C2 2012 January Q5
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}