| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2022 |
| Session | November |
| Marks | 8 |
| Topic | Function Transformations |
| Type | Multiple separate transformations (sketch-based, standard transformations) |
| Difficulty | Moderate -0.8 This question tests basic function transformation recall (horizontal translations and stretches) and reading solutions from a graph. Part (a) requires simple visual inspection of intersections, while part (b) involves standard textbook transformations with no problem-solving or novel insight required. The multiple parts and sketching add some work, but the concepts are fundamental and routine for A-level. |
| Spec | 1.02q Use intersection points: of graphs to solve equations1.02w Graph transformations: simple transformations of f(x) |
3.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{d8940254-0663-413e-a802-71519742cfcc-06_597_977_130_351}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
Figure 1 shows the graph of $y = \mathrm { f } ( x )$.
\begin{enumerate}[label=(\alph*)]
\item Write down the number of solutions that exist for the equation
\begin{enumerate}[label=(\roman*)]
\item $\mathrm { f } ( x ) = 1$,
\item $\mathrm { f } ( x ) = - x$.
\end{enumerate}\item Labelling the axes in a similar way, sketch on separate diagrams in the space provided the graphs of
\begin{enumerate}[label=(\roman*)]
\item $\quad y = \mathrm { f } ( x - 2 )$,
\item $y = \mathrm { f } ( 2 x )$.\\[0pt]
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM 2022 Q3 [8]}}