Answer
See graph and explanations.
Work Step by Step
To graph this function, we need to consider several different cases:
Case 1. $x\geq0$, we have $x+|y|=1+x$ or $|y|=1$ which gives $y=\pm1$, or two lines as shown in the figure.
Case 2. $x\lt0$, we have $-x+|y|=1+x$ or $|y|=2x+1$, which leads to two more cases:
(i) $y\geq0$, we have $y=2x+1$ shown as a line segment in the figure.
(ii) $y\lt0$, we have $-y=2x+1$ or $y=-2x-1$ shown as another line segment in the figure.
