Advanced MathMediumRange of a shifted square function
Advanced Math practice question
The function f is defined by f(x) = (x − 2)² + 3. Which of the following describes all possible values of f(x)?
- A. f(x) ≥ 3Correct
- B. f(x) ≤ 3
- C. f(x) ≥ 2
- D. All real numbers
Answer: A. f(x) ≥ 3
The square is at least 0, so f(x) is at least 3, reached at x = 2.
Why the other answers are wrong
- B. f(x) ≤ 3
- The parabola opens upward, so 3 is the minimum, not the maximum.
- C. f(x) ≥ 2
- 2 is the x-value of the vertex, not the minimum value.
- D. All real numbers
- Values below 3 are never reached.
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