I have had drawn this answer myself but I want clarification. What I do is:
\begin{cases} y = x-2 & \text{for } x\ge 1\\ \space \space = -x & \text{for }x<1 \end{cases}
\begin{cases} y = x-1 & \text{for } x\ge 0\\ \space \space = -x-1 & \text{for }x<0 \end{cases}
\begin{cases} y = x-3 & \text{for } x\ge 2\\ \space \space = -x+1 & \text{for }x<2 \end{cases}
Now we see that for $\space x<0, \;y=-x-1$ is the equation.
For $\; x\ge 0$ and $x\le \dfrac{1}{2},$ $y=x-1$ is the equation
For $\, x\ge \dfrac{1}{2},$ but $x<1$, we use $y=-x. $
For $\space x\ge 1 \space \text{and} x<\dfrac{3}{2}$ we have $y=x-2$.
For $\space x>\dfrac{3}{2} \space \text{and} x\le 2,$ we have $y=-x+1$
For $x>2$, we have $y=x-3$
Can anyone draw the graph and verify whether I am on the right track?