C3 June 2005 Q6

6.

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 \((1, a)\), \(a \lt 0\). One line meets the \(x\)-axis at \((3, 0)\). The other line meets the \(x\)-axis at \((-1, 0)\) and the \(y\)-axis at \((0, b)\), \(b \lt 0\).

In separate diagrams, sketch the graph with equation

Indicate clearly on each sketch the coordinates of any points of intersection with the axes.

Given that \(\mathrm{f}(x) = |x - 1| - 2\), find