What is the range of the function f(x) = 2 + sqrt(16 - x^2)?
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Correct answer
A. [2, 6]
Principle or equation
For a function involving a square root, the expression inside the root must be nonnegative. The range is determined by the minimum and maximum values of the square root term.
Why this answer is correct
The domain is x ∈ [-4, 4] because 16 - x^2 ≥ 0. The square root term sqrt(16 - x^2) ranges from 0 (when x = ±4) to 4 (when x = 0). Adding 2 gives a range from 2 to 6, inclusive. Thus the range is [2, 6].
Example
For f(x) = 3 + sqrt(9 - x^2), the range is [3, 6] because the sqrt term ranges from 0 to 3.
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