Edexcel P3 2020 January — Question 6

Exam BoardEdexcel
ModuleP3 (Pure Mathematics 3)
Year2020
SessionJanuary
TopicModulus function

6. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{1c700103-ecab-4a08-b411-3f445ed88885-18_736_1102_258_427} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} Figure 2 shows part of the graph with equation \(y = \mathrm { f } ( x )\), where $$\mathrm { f } ( x ) = 2 | 2 x - 5 | + 3 \quad x \geqslant 0$$ The vertex of the graph is at point \(P\) as shown.
  1. State the coordinates of \(P\).
  2. Solve the equation \(\mathrm { f } ( x ) = 3 x - 2\) Given that the equation $$f ( x ) = k x + 2$$ where \(k\) is a constant, has exactly two roots,
  3. find the range of values of \(k\).