Question

The range of the function \( f(x) = \sqrt{16 - x^2} \) is:

• A. [0, 4]
• B. [-4, 0]
• C. [-4, 4]
• D. (-4, 4)

Hint:

To determine the range of a square root function, identify the valid values of \( x \) and then calculate the possible output values.

Answer 1

The Correct Option is C

The function \( f(x) = \sqrt{16 - x^2} \) represents the positive square root of \( 16 - x^2 \). The domain is restricted to values where \( x^2 \leq 16 \), i.e., \( x \in [-4, 4] \). The square root function will give a range from 0 to 4, and the full range is from -4 to 4.