Final answer:
The correct equation that includes a reflection over the x-axis, a compression, a vertical shift up by 3 units, and a horizontal shift right by 4 units is C) f(x) = -√(x - 4) + 3.
Step-by-step explanation:
The student is asking us to find an equation for a reflected and compressed root function that also includes both a vertical and a horizontal shift. To reflect a root graph over the x-axis, we need a negative sign in front of the square root. A compression is not explicitly quantified, so we assume the compression is already included in the reflection. The vertical shift up is represented by adding 3 outside the function, and the horizontal shift right by 4 units is represented by subtracting 4 inside the function's argument before taking the square root.
The only option that reflects these transformations is C) f(x) = -√(x - 4) + 3. Here's why: The negative sign in front of the square root handles the reflection, the (x - 4) inside the square root accounts for the rightward shift by 4 units on the x-axis, and the plus 3 outside the square root accounts for the upward shift by 3 units on the y-axis.