Edexcel P3 2020 October — Question 4

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

4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{96948fd3-5438-4e95-b41b-2f649ca8dfac-10_780_839_123_557} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} Figure 2 shows a sketch of part of the graph with equation \(y = \mathrm { f } ( x )\) where $$\mathrm { f } ( x ) = 21 - 2 | 2 - x | \quad x \geqslant 0$$
  1. Find ff(6)
  2. Solve the equation \(\mathrm { f } ( x ) = 5 x\) Given that the equation \(\mathrm { f } ( x ) = k\), where \(k\) is a constant, has exactly two roots,
  3. state the set of possible values of \(k\). The graph with equation \(y = \mathrm { f } ( x )\) is transformed onto the graph with equation \(y = a \mathrm { f } ( x - b )\) The vertex of the graph with equation \(y = a \mathrm { f } ( x - b )\) is (6, 3). Given that \(a\) and \(b\) are constants,
  4. find the value of \(a\) and the value of \(b\). \includegraphics[max width=\textwidth, alt={}, center]{96948fd3-5438-4e95-b41b-2f649ca8dfac-11_2255_50_314_34}