What is the range of the function f(x) = 4 - 2x^2, where x is a real number?
Show the answer and explanation
Correct answer
A. (-∞, 4]
Principle or equation
For a quadratic function f(x) = ax^2 + bx + c with a < 0, the range is (-∞, maximum].
Why this answer is correct
f(x) = 4 - 2x^2. The maximum occurs at x = 0, giving f(0) = 4. As |x| increases, f(x) decreases without bound. So range is (-∞, 4].
Example
For f(x) = 1 - x^2, range is (-∞, 1].
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