14.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{aa75f1c1-ee97-4fee-af98-957e6a3fbba1-21_831_919_127_509}
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\caption{Figure 4}
\end{figure}
Figure 4 shows a sketch of the graph of \(y = g ( x ) , - 3 \leqslant x \leqslant 4\) and part of the line \(l\) with equation \(y = \frac { 1 } { 2 } x\)
The graph of \(y = \mathrm { g } ( x )\) consists of three line segments, from \(P ( - 3,4 )\) to \(Q ( 0,4 )\), from \(Q ( 0,4 )\) to \(R ( 2,0 )\) and from \(R ( 2,0 )\) to \(S ( 4,10 )\).
The line \(l\) intersects \(y = \mathrm { g } ( x )\) at the points \(A\) and \(B\) as shown in Figure 4.
- Use algebra to find the \(x\) coordinate of the point \(A\) and the \(x\) coordinate of the point \(B\).
Show each step of your working and give your answers as exact fractions.
- Sketch the graph with equation
$$y = \frac { 3 } { 2 } g ( x ) , \quad - 3 \leqslant x \leqslant 4$$
On your sketch show the coordinates of the points to which \(P , Q , R\) and \(S\) are transformed.