To determine the domain of the function $y = \sqrt{4x - 8}$, we must consider the condition under which the expression inside the square root is non-negative. The square root function is defined only for non-negative values.

Steps:

1. The condition for the square root to be defined is: $4x - 8 \geq 0$

2. Solve the inequality: $4x \geq 8 \quad \Rightarrow \quad x \geq 2$

Thus, the domain of the function is $x \geq 2$.

Correct Answer:

The correct choice is $x \geq 2$.

Would you like a deeper explanation or a graph of the function to illustrate this? Here are 5 related questions for further exploration:

1. What is the range of $y = \sqrt{4x - 8}$?
2. How do square root functions behave when their domain changes?
3. What happens if we change the function to $y = \sqrt{-4x + 8}$?
4. Can a square root function ever have negative outputs?
5. How would you express the domain and range of this function in interval notation?

Tip: Always check for restrictions like square roots and division by zero when determining a function's domain!