Final answer:
The calculated range for the function f(x) = x^3 - 22 - x with the domain {1, 2, 3} is {-22, -16, 2}. However, this set does not match any of the provided options, indicating there may be a typo in the question.
Step-by-step explanation:
To find the range of the function f(x) = x^3 - 22 - x when the domain is {1, 2, 3}, we substitute the values of the domain into the function.
- For x = 1: f(1) = 1^3 - 22 - 1 = 1 - 22 - 1 = -22
- For x = 2: f(2) = 2^3 - 22 - 2 = 8 - 22 - 2 = -16
- For x = 3: f(3) = 3^3 - 22 - 3 = 27 - 22 - 3 = 2
The range is the set of all resulting values, so the range for the given domain is {-22, -16, 2}. However, none of the provided options A, B, C, or D match this set. It's possible there might be a typo or error in the question since the calculated range does not match the given options. If the question was correctly transcribed and these are indeed the options provided, we must inform the student that there seems to be an issue.