How do you graph #abs(x+y)>1#?

1 Answer
Jul 19, 2018

There's plenty of ways one could do this, but let's just start by thinking about what this could look like.

We will think about the boundary of this region: #|x+y| = 1#.

Here we think about the two cases of absolute value: positive and negative.

If #x+y>0#, the boundary is simple:
#|x+y| = x+y = 1 implies y = -x + 1 #
which is just a line going down from (0,1) to (1,0).

If #x+y<0#, the boundary is another line:
#|x+y| = -(x+y) = 1 implies y = -x - 1 #
which is a line going from (-1,0) to (0, -1).

Therefore, there are three regions:
- Below the left line
- Between the lines
- Above the right line

It is clear that the more outside of those you get, the more #>1# you'll get, hence it is the regions outside the strip that are included.

In case my description wasn't sufficient, here's the plot:
graph{|x+y|=1 [-10, 10, -5, 5]}