AQA C3 2013 June — Question 7 9 marks

Exam BoardAQA
ModuleC3 (Core Mathematics 3)
Year2013
SessionJune
Marks9
PaperDownload PDF ↗
TopicFunction Transformations
TypeMultiple separate transformations (sketch-based, modulus involved)
DifficultyStandard +0.3 This is a standard C3 function transformation question requiring application of well-established rules: reflection in x-axis, horizontal stretch by factor 1/3, and reflection in y-axis for part (a); even function symmetry for part (b); and decomposing a composite transformation in part (c). All techniques are routine textbook exercises with no novel problem-solving required, making it slightly easier than average.
Spec1.02w Graph transformations: simple transformations of f(x)1.02x Combinations of transformations: multiple transformations

7 The diagram shows a sketch of the curve with equation \(y = \mathrm { f } ( x )\). \includegraphics[max width=\textwidth, alt={}, center]{063bbfa5-df49-44a1-8143-5e076397f63f-06_620_1216_356_422}
  1. On Figure 1, below, sketch the curve with equation \(y = - \mathrm { f } ( 3 x )\), indicating the values where the curve cuts the coordinate axes.
  2. On Figure 2, on page 7, sketch the curve with equation \(y = \mathrm { f } ( | x | )\), indicating the values where the curve cuts the coordinate axes.
  3. Describe a sequence of two geometrical transformations that maps the graph of \(y = \mathrm { f } ( x )\) onto the graph of \(y = \mathrm { f } \left( - \frac { 1 } { 2 } x \right)\). \begin{figure}[h]
    \captionsetup{labelformat=empty} \caption{Figure 1} \includegraphics[alt={},max width=\textwidth]{063bbfa5-df49-44a1-8143-5e076397f63f-06_732_1237_1649_443}
    \end{figure} \begin{figure}[h]
    \captionsetup{labelformat=empty} \caption{Figure 2} \includegraphics[alt={},max width=\textwidth]{063bbfa5-df49-44a1-8143-5e076397f63f-07_727_1211_340_466}
    \end{figure}

7 The diagram shows a sketch of the curve with equation $y = \mathrm { f } ( x )$.\\
\includegraphics[max width=\textwidth, alt={}, center]{063bbfa5-df49-44a1-8143-5e076397f63f-06_620_1216_356_422}
\begin{enumerate}[label=(\alph*)]
\item On Figure 1, below, sketch the curve with equation $y = - \mathrm { f } ( 3 x )$, indicating the values where the curve cuts the coordinate axes.
\item On Figure 2, on page 7, sketch the curve with equation $y = \mathrm { f } ( | x | )$, indicating the values where the curve cuts the coordinate axes.
\item Describe a sequence of two geometrical transformations that maps the graph of $y = \mathrm { f } ( x )$ onto the graph of $y = \mathrm { f } \left( - \frac { 1 } { 2 } x \right)$.

\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Figure 1}
  \includegraphics[alt={},max width=\textwidth]{063bbfa5-df49-44a1-8143-5e076397f63f-06_732_1237_1649_443}
\end{center}
\end{figure}

\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Figure 2}
  \includegraphics[alt={},max width=\textwidth]{063bbfa5-df49-44a1-8143-5e076397f63f-07_727_1211_340_466}
\end{center}
\end{figure}
\end{enumerate}

\hfill \mbox{\textit{AQA C3 2013 Q7 [9]}}