Edexcel P3 2022 June — Question 5

Exam BoardEdexcel
ModuleP3 (Pure Mathematics 3)
Year2022
SessionJune
TopicModulus function

5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{44035bf8-f54c-472a-b969-b4fa4fa3d203-14_668_812_258_566} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} Figure 2 shows part of the graph with equation \(y = \mathrm { f } ( x )\), where $$\mathrm { f } ( x ) = | k x - 9 | - 2 \quad x \in \mathbb { R }$$ and \(k\) is a positive constant. The graph intersects the \(y\)-axis at the point \(A\) and has a minimum point at \(B\) as shown.
    1. Find the \(y\) coordinate of \(A\)
    2. Find, in terms of \(k\), the \(x\) coordinate of \(B\)
  1. Find, in terms of \(k\), the range of values of \(x\) that satisfy the inequality $$| k x - 9 | - 2 < 0$$ Given that the line \(y = 3 - 2 x\) intersects the graph \(y = \mathrm { f } ( x )\) at two distinct points,
  2. find the range of possible values of \(k\)