Sketch the region of the points satisfying `max. {|x|, |y|} le 4`.

Explanation

We have `max. {|x|,|y|} le 4`.
When `|y| le 4,` we have `|x| lt |y|" "` (i)
The points satisfying the above inequalities are shown in the following figure. ltBrgt
`" "|x| le 4`, when `|y| lt |x|" "` (ii)
The points satisfying the above inequalities are shown in the following figure.

Combining the above two regions, we have the square as shown in the following figure.