6.
\begin{figure}[h]
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\caption{Figure 1}
\includegraphics[alt={},max width=\textwidth]{5af2eea6-bac1-455b-b25a-487d113e44ca-08_458_876_285_539}
\end{figure}
Figure 1 shows part of the graph of \(y = \mathrm { f } ( x ) , x \in \mathbb { R }\). The graph consists of two line segments that meet at the point \(( 1 , a ) , a < 0\). One line meets the \(x\)-axis at \(( 3,0 )\). The other line meets the \(x\)-axis at \(( - 1,0 )\) and the \(y\)-axis at \(( 0 , b ) , b < 0\).
In separate diagrams, sketch the graph with equation
- \(y = \mathrm { f } ( x + 1 )\),
- \(y = \mathrm { f } ( | x | )\).
Indicate clearly on each sketch the coordinates of any points of intersection with the axes.
Given that \(\mathrm { f } ( x ) = | x - 1 | - 2\), find
- the value of \(a\) and the value of \(b\),
- the value of \(x\) for which \(\mathrm { f } ( x ) = 5 x\).