Answer:
-5 ≤ y < ∞.
Explanation:
The range of a function is the set of all possible output values (y-values) of the function. To find the range of f(x) = |x| − 5, we can first consider what happens when x is positive. In this case, the absolute value of x is just x, so the function becomes f(x) = x − 5. For example, if x = 6, then f(x) = 6 - 5 = 1. We can do this for any positive value of x to find the y-values that the function produces when x is positive.
Next, we can consider what happens when x is negative. In this case, the absolute value of x is -x, so the function becomes f(x) = -x - 5. For example, if x = -6, then f(x) = -6 - 5 = -11. We can do this for any negative value of x to find the y-values that the function produces when x is negative.
We can then combine the y-values that the function produces when x is positive and negative to find the range of the function. Since the function produces all y-values greater than or equal to -5 when x is positive and all y-values less than or equal to -5 when x is negative, the range of the function is -5 ≤ y ≤ ∞.
Therefore, the correct answer is -5 ≤ y < ∞.