| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2020 |
| Session | February |
| Marks | 11 |
| Topic | Function Transformations |
| Type | Algebraic to algebraic transformation description |
| Difficulty | Moderate -0.3 This is a multi-part question covering standard function transformations and composition. Part (a) requires describing transformations of a line (reflection and translation), parts (b-d) involve routine function composition and domain determination, and part (e) asks for an inverse function. While comprehensive, all components are textbook exercises requiring no novel insight—slightly easier than average due to straightforward algebraic manipulation throughout. |
| Spec | 1.02u Functions: definition and vocabulary (domain, range, mapping)1.02v Inverse and composite functions: graphs and conditions for existence1.02w Graph transformations: simple transformations of f(x)1.02x Combinations of transformations: multiple transformations |
9
\begin{enumerate}[label=(\alph*)]
\item Describe fully a sequence of transformations that map the line $y = x$ onto the line
$$y = 10 - 2 x$$
The function f is defined as $\mathrm { f } : x \rightarrow 10 - 2 x , x \in R , x \geq 0$.\\
The function ff is denoted by g .
\item Find $\mathrm { g } ( x )$, giving your answer in a form without brackets.
\item Determine the domain of g .
\item Explain whether $\mathrm { fg } = \mathrm { gf }$.
\item Find $\mathrm { g } ^ { - 1 }$ in the form $\mathrm { g } ^ { - 1 } : x \rightarrow \ldots$
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Pure 2020 Q9 [11]}}