Question

Given: f(x) = -√(16 - x²), find f(x). Then state whether y(x) is a function.

A) f(x) = -√(16 - x²); y(x) is a function.
B) f(x) = -√(16 - x²); y(x) is not a function.
C) f(x) = √(16 - x²); y(x) is a function.
D) f(x) = √(16 - x²); y(x) is not a function.

Answer 1

The given function f(x) = -√(16 - x²) is indeed a function because it passes the vertical line test, meaning for each x-value there is only one y-value.

Step-by-step explanation:

The function given is f(x) = -√(16 - x²). To determine whether y(x) is a function, we can apply the vertical line test, which states that if a vertical line intersects the graph of the equation at more than one point, then the graph does not represent a function. Since the square root function (√) inherently passes the vertical line test (because for each x-value there is only one y-value), y(x) is indeed a function. However, because we have a negative square root function, the output is always negative or zero, within the domain of real numbers that satisfy 16 - x² ≥ 0. This implies that for each x, there is only one y value, satisfying the definition of a function.

The correct answer is A) f(x) = -√(16 - x²); y(x) is a function.