Given the function;
[tex]y=|x+2|-2[/tex]
The range of the function can be derived by finding the lowest and highest possible value of the function.
For the function, the lowest value is at;
[tex]|x+2|=0[/tex]
Since |x+2| cannot be less than zero.
So, The lowest value of y is;
[tex]\begin{gathered} y=|x+2|-2 \\ y=0-2 \\ y=-2 \end{gathered}[/tex]
The highest value is infinity, because the higher the value of |x+2| the higher the value of the function.
Therefore, the range of the function is;
[tex]y\ge-2[/tex]
Because the lowest possible value is -2 and the highest possible value is infinity.
