SPS SPS SM Pure 2024 June — Question 6

Exam BoardSPS
ModuleSPS SM Pure (SPS SM Pure)
Year2024
SessionJune
TopicCurve Sketching
TypeSolutions from graphical analysis

6. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{b063f4ea-372b-4193-b8fe-a9f8017d7349-12_735_1081_239_500} \captionsetup{labelformat=empty} \caption{Figure 1}
\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.
  1. Using Figure 1, find the range of values of \(x\) for which $$f ( x ) < 6$$
  2. State the largest solution of the equation $$f ( 2 x ) = 6$$
    1. 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.
    2. Hence, using set notation, find the set of values of \(x\) for which $$f ( - x ) \geq 6 \text { and } x < 0$$