Question

How do you graph `absx<=absy`?

Answer 1

See below...

Explanation:

One way to understand what `absx<=absy` is to see that, within the absolute value sign, we can have both positive and negative values. So let's rewrite this to be:

`pmx<=pmy`

So what does this actually mean? Let's first graph the lines themselves and then work on shading next:

graph{(y-x)(y+x)=0}

Now for the shading.

When `x=0, y=0`

When `x=1, y<=1, -1=>y<=1`

When `x=-1, y<=1, -1=>y<=1`

So if we see the X in the graph, we want to shade all but the top slice (I can't get the graphing tool to shade properly...)