|x|+|y|= 2

This implies that two non-negative quatities add up to 2,
so neither x nor y can be greater than 2 nor less than -2.
So the domain and range are both [-2,2].

The only points with integers for both coordinates are
( x, y)
-------
{-2, 0)
{-1,-1)
{-1, 1)
{ 0,-2)
{ 0, 2)
{ 1,-1)
{ 1, 1)
{ 2, 0)

Plot them:



Sketch in the graph.  It is a diamond (or square turned sideways):



Edwin