SPS SPS SM Mechanics 2022 February — Question 10

Exam BoardSPS
ModuleSPS SM Mechanics (SPS SM Mechanics)
Year2022
SessionFebruary
TopicModulus function

10. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{eacf7695-44c4-4937-8e92-5b0df8ad5f70-24_707_716_255_826} \captionsetup{labelformat=empty} \caption{Figure 4}
\end{figure} Figure 4 shows a sketch of the graph with equation $$y = | 2 x - 3 k |$$ where \(k\) is a positive constant.
  1. Sketch the graph with equation \(y = \mathrm { f } ( x )\) where $$\mathrm { f } ( x ) = k - | 2 x - 3 k |$$ stating
    • the coordinates of the maximum point
    • the coordinates of any points where the graph cuts the coordinate axes
    • Find, in terms of \(k\), the set of values of \(x\) for which
    $$k - | 2 x - 3 k | > x - k$$ giving your answer in set notation.
  2. Find, in terms of \(k\), the coordinates of the minimum point of the graph with equation $$y = 3 - 5 \mathrm { f } \left( \frac { 1 } { 2 } x \right)$$ [BLANK PAGE]
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