Graphing inequality with mod function

[aim1732]

How can we graph this inequality - |y|+1/2>=e^-|x| ?
I drew the function(actually a combination of functions) for equality. It would be symmetric in all quadrants and intersect the axes at +ln2 and -ln2(x-axis) and 1/2 and -1/2(y-axis).However since the various graphs are mixed up it is hard pinpoint what region to take.

I have attached one half of the actual graph.
The other half is it's reflection on the x-axis.

 

[Mark44]

How can we graph this inequality - |y|+1/2>=e^-|x| ?
I drew the function(actually a combination of functions) for equality. It would be symmetric in all quadrants and intersect the axes at +ln2 and -ln2(x-axis) and 1/2 and -1/2(y-axis).However since the various graphs are mixed up it is hard pinpoint what region to take.

I have attached one half of the actual graph.
The other half is it's reflection on the x-axis.

Your inequality is equivalent to |y| >= e^-|x| - 1/2. This can be rewritten as
y >= e^-|x| - 1/2 or -y >= e^-|x| - 1/2

So y >= e^-|x| - 1/2 or y <= -e^-|x| + 1/2

Does that help?

 

[aim1732]

Yes I should have considered the intervals for the different inequalities.Thanks a lot.