Question

sketch the region 0<|y|+|x|<1

Answer 1

Evaluate each of four quadrants
a) Quadrant I: y>0; x>0
0< y + x < 1 => y < 1-x (Sketch y=1-x)
b) Quadrant II: y>0, x < 0
0<y-x<1 => y < 1+x (Sketch y=1+x)
So on, we have:
c) Quadrant III: -y < 1+x (Sketch y= -(1+x))
d) Quadrant IV: y>x-1 (Sketch y = x-1)

So, 0<|y|+|x|<1 is the rhombus with 4 boundaries formed by 4 lines, having the center at (0,0)