Edexcel P3 2021 October — Question 2

Exam BoardEdexcel
ModuleP3 (Pure Mathematics 3)
Year2021
SessionOctober
TopicModulus function

2. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{9b0b8db0-79fd-4ad5-88c9-737447d9f894-06_570_604_255_673} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows a sketch of part of the graph with equation \(y = \mathrm { f } ( x )\), where $$f ( x ) = | 3 x - 13 | + 5 \quad x \in \mathbb { R }$$ The vertex of the graph is at point \(P\), as shown in Figure 1.
  1. State the coordinates of \(P\).
    1. State the range of f .
    2. Find the value of ff(4)
  2. Solve, using algebra and showing your working, $$16 - 2 x > | 3 x - 13 | + 5$$ 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 \(( 4,20 )\) Given that \(a\) and \(b\) are constants,
  3. find the value of \(a\) and the value of \(b\).