Describe transformation from graph

A question is this type if and only if it shows two graphs (one solid, one dashed or labeled differently) and asks to describe or state the transformation or equation of the transformed graph.

5 questions

CAIE P1 2020 June Q3
3 In each of parts (a), (b) and (c), the graph shown with solid lines has equation \(y = \mathrm { f } ( x )\). The graph shown with broken lines is a transformation of \(y = \mathrm { f } ( x )\).

  1. \includegraphics[max width=\textwidth, alt={}, center]{aa4c496d-ce5f-4f46-ad37-d901644a9e7c-04_412_645_367_788} State, in terms of f , the equation of the graph shown with broken lines.

  2. \includegraphics[max width=\textwidth, alt={}, center]{aa4c496d-ce5f-4f46-ad37-d901644a9e7c-04_650_423_1046_900} State, in terms of f , the equation of the graph shown with broken lines.

  3. \includegraphics[max width=\textwidth, alt={}, center]{aa4c496d-ce5f-4f46-ad37-d901644a9e7c-04_550_631_1975_804} State, in terms of f , the equation of the graph shown with broken lines.
OCR MEI C1 Q2
2 \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{91e16597-234a-4730-8c4b-765ca574e6e2-1_522_528_867_803} \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 \(B\) ? $$\begin{aligned} & y = \mathrm { f } ( x ) + 2
    & y = 2 \mathrm { f } ( x ) \end{aligned}$$ $$\begin{aligned} & y = \mathrm { f } ( x ) - 2
    & y = \mathrm { f } ( x + 3 ) \end{aligned}$$ $$\begin{aligned} & y = \mathrm { f } ( x + 2 )
    & y = \mathrm { f } ( x - 3 ) \end{aligned}$$
OCR MEI C3 2012 January Q5
5 Each of the graphs of \(y = \mathrm { f } ( x )\) and \(y = \mathrm { g } ( x )\) below is obtained using a sequence of two transformations applied to the corresponding dashed graph. In each case, state suitable transformations, and hence find expressions for \(\mathrm { f } ( x )\) and \(\mathrm { g } ( x )\).

  1. \includegraphics[max width=\textwidth, alt={}, center]{8b8958be-0ebc-4f72-ac3f-c16a8ec9e4ab-2_430_712_1366_680}

  2. \includegraphics[max width=\textwidth, alt={}, center]{8b8958be-0ebc-4f72-ac3f-c16a8ec9e4ab-2_394_608_1925_731}
AQA AS Paper 2 Specimen Q2
1 marks
2 The graph of \(y = \mathrm { f } ( x )\) is shown in Figure 1. \begin{figure}[h]
\captionsetup{labelformat=empty} \caption{Figure 1} \includegraphics[alt={},max width=\textwidth]{f2bf5e19-98ba-4047-9023-3cfe20987e01-03_536_849_664_735}
\end{figure} State the equation of the graph shown in Figure 2. \begin{figure}[h]
\captionsetup{labelformat=empty} \caption{Figure 2} \includegraphics[alt={},max width=\textwidth]{f2bf5e19-98ba-4047-9023-3cfe20987e01-03_532_851_1530_733}
\end{figure} Circle your answer.
[0pt] [1 mark] $$y = \mathrm { f } ( 2 x ) \quad y = \mathrm { f } \left( \frac { x } { 2 } \right) \quad y = 2 \mathrm { f } ( x ) \quad y = \frac { 1 } { 2 } \mathrm { f } ( x )$$
AQA Further AS Paper 1 2021 June Q13
4 marks
13 Prove by induction that, for all integers \(n \geq 1\) $$\sum _ { r = 1 } ^ { n } 2 ^ { - r } = 1 - 2 ^ { - n }$$ [4 marks]