Multiple choice transformation

6

1. The diagrams show five different graphs. In each case the whole of the graph is shown. \begin{figure}[h]
   \includegraphics[alt={},max width=\textwidth]{cb83836f-753f-4b3a-99e8-a18aff0f49ff-06_376_382_310_306} \captionsetup{labelformat=empty} \caption{Fig. 1.1}
   \end{figure} \begin{figure}[h]
   \includegraphics[alt={},max width=\textwidth]{cb83836f-753f-4b3a-99e8-a18aff0f49ff-06_376_378_310_842} \captionsetup{labelformat=empty} \caption{Fig. 1.2}
   \end{figure} \begin{figure}[h]
   \includegraphics[alt={},max width=\textwidth]{cb83836f-753f-4b3a-99e8-a18aff0f49ff-06_378_378_310_1379} \captionsetup{labelformat=empty} \caption{Fig. 1.3}
   \end{figure} \begin{figure}[h]
   \includegraphics[alt={},max width=\textwidth]{cb83836f-753f-4b3a-99e8-a18aff0f49ff-06_378_382_872_306} \captionsetup{labelformat=empty} \caption{Fig. 1.4}
   \end{figure} \begin{figure}[h]
   \includegraphics[alt={},max width=\textwidth]{cb83836f-753f-4b3a-99e8-a18aff0f49ff-06_378_378_872_845} \captionsetup{labelformat=empty} \caption{Fig. 1.5}
   \end{figure} Place ticks in the boxes in the table in the Printed Answer Booklet to indicate, for each graph, whether it represents a one-one function, a many-one function, a function that is its own inverse or it does not represent a function. There may be more than one tick in some rows or columns of the table.
2. A function f is defined by \(\mathrm { f } ( x ) = \frac { 1 } { x }\) for the domain \(\{ x : 0 < x \leqslant 2 \}\). State the range of f , giving your answer in set notation.

3 The curve $$y = \log _ { 4 } x$$ is transformed by a stretch, scale factor 2 , parallel to the \(y\)-axis.
State the equation of the curve after it has been transformed.
Circle your answer.
[0pt] [1 mark] $$y = \frac { 1 } { 2 } \log _ { 4 } x \quad y = 2 \log _ { 4 } x \quad y = \log _ { 4 } 2 x \quad y = \log _ { 8 } x$$

3 The curve with equation \(y = \ln x\) is transformed by a stretch parallel to the \(x\)-axis with scale factor 2 Find the equation of the transformed curve.
Circle your answer. \(y = \frac { 1 } { 2 } \ln x \quad y = 2 \ln x \quad y = \ln \frac { x } { 2 } \quad y = \ln 2 x\)

The curve \(y = \sqrt{x}\) is translated onto the curve \(y = \sqrt{x + 4}\) The translation is described by a vector. Find this vector. Circle your answer. [1 mark] \(\begin{bmatrix} 4 \\ 0 \end{bmatrix}\) \(\begin{bmatrix} -4 \\ 0 \end{bmatrix}\) \(\begin{bmatrix} 0 \\ 4 \end{bmatrix}\) \(\begin{bmatrix} 0 \\ -4 \end{bmatrix}\)

Figure 1 shows \(y = f(x)\). \includegraphics{figure_1} Which figure below shows \(y = f(2x)\)? Tick one box. \includegraphics{figure_2} \quad \includegraphics{figure_3} \quad \includegraphics{figure_4} \quad \includegraphics{figure_5} [1 mark]

The graph of \(y = f(x)\) is shown in Figure 1. \includegraphics{figure_1} State the equation of the graph shown in Figure 2. \includegraphics{figure_2} Circle your answer. [1 mark] \(y = f(2x)\) \quad\quad \(y = f\left(\frac{x}{2}\right)\) \quad\quad \(y = 2f(x)\) \quad\quad \(y = \frac{1}{2}f(x)\)