7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e30f0c28-1695-40a1-8e9a-6ea7e29042bf-12_458_433_264_781}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
Figure 2 shows a sketch of the graph of \(y = \mathrm { f } ( x ) , x \in \mathbb { R }\).
The point \(P \left( \frac { 1 } { 3 } , 0 \right)\) is the vertex of the graph.
The point \(Q ( 0,5 )\) is the intercept with the \(y\)-axis.
Given that \(\mathrm { f } ( x ) = | a x + b |\), where \(a\) and \(b\) are constants,
- find all possible values for \(a\) and \(b\),
- hence find an equation for the graph.
- Sketch the graph with equation
$$y = \mathrm { f } \left( \frac { 1 } { 2 } x \right) + 3$$
showing the coordinates of its vertex and its intercept with the \(y\)-axis.