The range of a function is the set of all possible outputs (y-values) for a given input (x-value).
Given the function f(x) = [x+3]-5, we can see that the function first adds 3 to x and then subtracts 5. The square bracket notation around (x+3) indicates that the function is taking the greatest integer less than or equal to (x+3).
For any input x, the output of the function will always be the greatest integer less than or equal to (x+3) - 5. Therefore, the output of the function is always an integer less than or equal to -2.
So the range of the function is [-5, -2] U (-2, ∞)
Option A) [-5,∞) is incorrect as the range starts with -5 but the function output is always less than or equal to -2.
Option B) (-5,∞) is incorrect as the function output is always less than or equal to -2.
Option C) [3,∞) is incorrect as the function output is always less than or equal to -2.
Option D) (3,∞) is incorrect as the function output is always less than or equal to -2.
The correct answer is (-2, ∞)