5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{42aff260-e734-48ff-a92a-674032cb0377-16_561_848_214_699}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
Figure 2 shows part of the graph with equation \(y = \mathrm { f } ( x )\), where
$$\mathrm { f } ( x ) = 2 | 5 - x | + 3 , \quad x \geqslant 0$$
Given that the equation \(\mathrm { f } ( x ) = k\), where \(k\) is a constant, has exactly one root,
- state the set of possible values of \(k\).
- Solve the equation \(\mathrm { f } ( x ) = \frac { 1 } { 2 } x + 10\)
The graph with equation \(y = \mathrm { f } ( x )\) is transformed onto the graph with equation \(y = 4 \mathrm { f } ( x - 1 )\). The vertex on the graph with equation \(y = 4 \mathrm { f } ( x - 1 )\) has coordinates \(( p , q )\).
- State the value of \(p\) and the value of \(q\).