The equation of f(x) is B. F(x) = -√x. Therefore , B. F(x) = -√x is correct.
Here's why:
The parent function of the graph is the square root function, which means the original equation is f(x) = √x.
The graph is reflected across the x-axis.
This means that the y-values are multiplied by -1. In other words, if the original point was (x, √x), the reflected point would be (x, -√x).
Therefore, the equation of the reflected function is f(x) = -√x.
The other options are incorrect because:
A. F(x) = √x is the original equation, not the reflected equation.
C. F(x) = √x - 1 shifts the graph down one unit, but it does not reflect it across the x-axis.
D. F(x) = √x + 1 shifts the graph up one unit, but it does not reflect it across the x-axis.