How do you graph #absx<=absy#?

1 Answer

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...)