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Reviewed CSCA Mathematics question · Standard

What is the range of the function f(x) = 4 - sqrt(25 - x^2)?

  1. [-1, 4]
  2. [0, 4]
  3. [-1, 9]
  4. [4, 9]
Show the answer and explanation

Correct answer

A. [-1, 4]

Principle or equation

The range of a function involving a square root is determined by the possible values of the square root expression.

Why this answer is correct

The expression under the square root, 25 - x^2, ranges from 0 to 25 as x varies over [-5, 5]. Thus sqrt(25 - x^2) ranges from 0 to 5. Then f(x) = 4 - sqrt(...) ranges from 4 - 5 = -1 to 4 - 0 = 4. So the range is [-1, 4].

Example

For f(x) = 2 - sqrt(9 - x^2), sqrt ranges 0 to 3, so range is [-1, 2].

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