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
$$\mathrm { f } ( x ) = 21 - 2 | 2 - x | \quad x \geqslant 0$$
- Find ff(6)
- 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,
- 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,
- 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}