SPS SPS FM Pure 2023 November — Question 8

Exam BoardSPS
ModuleSPS FM Pure (SPS FM Pure)
Year2023
SessionNovember
TopicModulus function

8. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{3dcde139-bc6b-412d-8d1f-c45543d67430-16_703_851_150_701} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} Figure 2 shows a sketch of the graph with equation $$y = 2 | x + 4 | - 5$$ The vertex of the graph is at the point \(P\), shown in Figure 2.
  1. Find the coordinates of \(P\).
  2. Solve the equation $$3 x + 40 = 2 | x + 4 | - 5$$ A line \(l\) has equation \(y = a x\), where \(a\) is a constant.
    Given that \(l\) intersects \(y = 2 | x + 4 | - 5\) at least once,
  3. find the range of possible values of \(a\), writing your answer in set notation.
    [0pt] [BLANK PAGE]