3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f47675f8-a2c2-4c4c-b878-ffe15a95c19d-05_623_977_207_479}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows the graph of \(y = f ( x ) , x \in \mathbb { R }\).
The graph consists of two line segments that meet at the point \(P\).
The graph cuts the \(y\)-axis at the point \(Q\) and the \(x\)-axis at the points \(( - 3,0 )\) and \(R\). Sketch, on separate diagrams, the graphs of
- \(y = | f ( x ) |\),
- \(y = \mathrm { f } ( - x )\).
Given that \(\mathrm { f } ( x ) = 2 - | x + 1 |\),
- find the coordinates of the points \(P , Q\) and \(R\),
- solve \(\mathrm { f } ( x ) = \frac { 1 } { 2 } x\).