Final answer:
The vertex of the absolute value function |2x - 2| occurs at the point where the inside of the absolute value is zero, resulting in the vertex (1, 0). None of the provided answers match the correct vertex.
Step-by-step explanation:
The absolute value function in question is |2x - 2|, which is a piecewise-linear function with a 'V' shape. The vertex of this function is the point where the direction of the function changes, which occurs where the expression inside the absolute value becomes zero. Therefore, we set the inside of the absolute value to zero:
2x - 2 = 0
2x = 2
x = 1
Substituting x = 1 back into the function |2x - 2|, we get |2(1) - 2| = |0| = 0. The vertex of the function is the point (x, |2x - 2|). Therefore, the vertex of the given absolute value function is (1, 0). None of the provided answer choices A) (4, -1), B) (1, 4), C) (1, -4), or D) (4, 1) are correct.