| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2024 |
| Session | June |
| Marks | 6 |
| Topic | Curve Sketching |
| Type | Solutions from graphical analysis |
| Difficulty | Moderate -0.8 This question tests basic graph transformations and reading values from a curve. Part (a) requires reading where the curve is below y=6. Part (b) involves a horizontal stretch (routine transformation). Part (c) involves reflection in y-axis and combining inequalities with set notation. All parts are standard graphical analysis with no complex reasoning or calculation required. |
| Spec | 1.02m Graphs of functions: difference between plotting and sketching1.02w Graph transformations: simple transformations of f(x) |
6.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{b063f4ea-372b-4193-b8fe-a9f8017d7349-12_735_1081_239_500}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
Figure 1 shows the curve with equation $y = \mathrm { f } ( x )$.\\
The points $P ( - 4,6 ) , Q ( - 1,6 ) , R ( 2,6 )$ and $S ( 3,6 )$ lie on the curve.
\begin{enumerate}[label=(\alph*)]
\item Using Figure 1, find the range of values of $x$ for which
$$f ( x ) < 6$$
\item State the largest solution of the equation
$$f ( 2 x ) = 6$$
\item \begin{enumerate}[label=(\roman*)]
\item Sketch the curve with equation $y = \mathrm { f } ( - x )$.
On your sketch, state the coordinates of the points to which $P , Q , R$ and $S$ are transformed.
\item Hence, using set notation, find the set of values of $x$ for which
$$f ( - x ) \geq 6 \text { and } x < 0$$
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Pure 2024 Q6 [6]}}