| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2023 |
| Session | January |
| Marks | 4 |
| Topic | Function Transformations |
| Type | Sequence of transformations order |
| Difficulty | Moderate -0.3 This is a straightforward transformations question requiring standard application of function transformation rules. Part (i) involves applying two transformations sequentially to ln x (reflection then translation), which is routine. Part (ii) requires working backwards from the transformed equation to identify the sequence, but the algebra is simple and the transformations are given. Both parts are mechanical applications of A-level transformation techniques with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.02w Graph transformations: simple transformations of f(x)1.02x Combinations of transformations: multiple transformations |
The transformations $\mathbf{R}$, $\mathbf{S}$ and $\mathbf{T}$ are defined as follows.
\begin{align}
\mathbf{R} &: \quad \text{reflection in the } x\text{-axis} \\
\mathbf{S} &: \quad \text{stretch in the } x\text{-direction with scale factor } 3 \\
\mathbf{T} &: \quad \text{translation in the positive } x\text{-direction by } 4 \text{ units}
\end{align}
\begin{enumerate}[label=(\roman*)]
\item The curve $y = \ln x$ is transformed by $\mathbf{R}$ followed by $\mathbf{T}$. Find the equation of the resulting curve. [2]
\item Find, in terms of $\mathbf{S}$ and $\mathbf{T}$, a sequence of transformations that transforms the curve $y = x^3$ to the curve $y = \left(\frac{1}{3}x - 4\right)^3$. You should make clear the order of the transformations. [2]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM 2023 Q2 [4]}}