First of all we know the Absolute Value Function that is:
[tex]\left | x \right |= \left \{ {{x \ \ \ \ x \geq 0} \atop {-x \ \ \ \ x\ \textless \ 0}} \right. [/tex]
This is called the Parent Function of the Absolute Value Function.
From the equation:
[tex]y=\left | x+2 \right |-3[/tex]
The term:
[tex]\left | x+2 \right |[/tex]
means that the the Parent Function is shifted two units to the left.
On the other hand, the term:
[tex]-3[/tex]
means that the function [tex]\left | x+2 \right |[/tex] is shifted three units downward. So the result is the graph shown below
Conclusion: The graph is the second one.
