2.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{9b0b8db0-79fd-4ad5-88c9-737447d9f894-06_570_604_255_673}
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\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.
- State the coordinates of \(P\).
- State the range of f .
- Find the value of ff(4)
- 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,
- find the value of \(a\) and the value of \(b\).