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Reviewed CSCA Mathematics question · Easy

What is the range of the function f(x) = 5 - 3x^2?

  1. (-∞, 5]
  2. [5, ∞)
  3. (-∞, 5)
  4. (-∞, ∞)
Show the answer and explanation

Correct answer

A. (-∞, 5]

Principle or equation

The range of a quadratic function with a negative leading coefficient is (-∞, maximum value].

Why this answer is correct

The function f(x) = 5 - 3x^2 is a downward-opening parabola with vertex at (0, 5). The maximum value is 5, and as x increases in magnitude, the function decreases without bound. Therefore, the range is (-∞, 5].

Example

For g(x) = 2 - x^2, the range is (-∞, 2].

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