What is the range of the function y=|x+2| -2 if the domain is x e R

Question

asked Dec 7, 2023 78.0k views

1 Answer

Gil Adirim · Answer 1 · 2023-12-13T08:34:22+0000

Given the function;

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;

Since |x+2| cannot be less than zero.

So, The lowest value of y is;

$\begin{gathered} y=|x+2|-2 \\ y=0-2 \\ y=-2 \end{gathered}$

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;

$y\ge-2$

Because the lowest possible value is -2 and the highest possible value is infinity.