| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2025 |
| Session | October |
| Marks | 4 |
| Topic | Function Transformations |
| Type | Identify/describe sequence of transformations between two given equations |
| Difficulty | Moderate -0.8 This is a straightforward transformations question requiring recall of standard rules: horizontal stretch by factor 1/2 transforms e^x to e^(2x), then translation by vector (1/2, 0), and vertical stretch by factor 1/e. All transformations are routine applications of A-level formulas with no problem-solving or insight required, making it easier than average. |
| Spec | 1.02w Graph transformations: simple transformations of f(x) |
The graph of $y = \text{e}^x$ can be transformed to the graph of $y = \text{e}^{2x-1}$ by a stretch parallel to the $x$-axis followed by a translation.
\begin{enumerate}[label=(\alph*)]
\item
\begin{enumerate}[label=(\roman*)]
\item State the scale factor of the stretch. [1]
\item Give full details of the translation. [2]
\end{enumerate}
\end{enumerate}
Alternatively the graph of $y = \text{e}^x$ can be transformed to the graph of $y = \text{e}^{2x-1}$ by a stretch parallel to the $x$-axis and a stretch parallel to the $y$-axis.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item State the scale factor of the stretch parallel to the $y$-axis. [1]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM 2025 Q10 [4]}}