What is the range of the function f(x) = 3 - 2x^2, where x is a real number?
Show the answer and explanation
Correct answer
A. (-∞, 3]
Principle or equation
The range of a quadratic function with negative leading coefficient is (-∞, maximum value].
Why this answer is correct
The function is a downward-opening parabola with vertex at (0,3). The maximum value is 3, and as x increases in magnitude, f(x) decreases without bound. Thus range is (-∞, 3].
Example
For f(x) = 1 - x^2, range is (-∞, 1].
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