Problem: Draw the region of points in the plane, which satisfy .
Solution: region will bounded by lines , , & . Why is that?
First note that \( |x| \le 1 \) implies:
Similarly, if we demand \( |y| \le 1 \) (the double shaded zone).
Now if we want \( |y| \le |x| \) . This can be achieved by
- \( y \le x \) when x and y are both positive (in the first quadrant); that is the region below the line x = y
- \( y \le -x\) when x is negative and y positive (in the second quadrant); hence the region below the line y = -x
- \(-y \le -x \) when (x, y) is in the third quadrant.
- \( -y \le x \) when (x, y) is in fourth quadrant.
Therefore the final region is the following shaded region: