Given the following absolute value function find the range f (x) = |x+5|-8

The minimum value for |x+5| is 0, so the minimum for f (x) is 0-8=-8.

There is no maximum for |x+5|, so neither does f (x).

Therefore the range of f (x) = |x+5|-8 is [-8,+inf) in interval notation, or

from - 8 to infinity in words.