The Range of the function f(x) = (x - 2) / (2 - x) is....
2024
The Range of the function f(x) = (x - 2) / (2 - x) is....
- A.
-1 to 1
- B.
0 to 1
- C.
-1 to 0
- D.
None of the above
Attempted by 1 students.
Show answer & explanation
Correct answer: D
Solution: Simplify the expression and determine the domain and outputs.
Note that 2 - x = -(x - 2).
Therefore for x ≠ 2, f(x) = (x - 2)/(2 - x) = (x - 2)/-(x - 2) = -1.
At x = 2 the function is undefined (division by zero), so x = 2 is not in the domain.
Thus the function takes the single value -1 for every allowed x, and the range is the set {-1}.
Because the provided interval choices are not the single value {-1}, the correct choice is the option that states 'None of the above'.