Final answer:
The vertex of the absolute value function f(x) = -|x-a| + b is at the coordinate point (a, b), reflecting the standard form of an absolute value function with vertex at (h, k). The transformations applied to the function do not alter the position of the vertex, making option c) (a, b) the correct answer.
Step-by-step explanation:
The vertex of the absolute value function f(x) = -|x-a| + b where a and b are real numbers can be determined by understanding the standard form of an absolute value function, which is f(x) = |x - h| + k. In this standard form, the vertex is at the point (h, k). Comparing this with the given function, we can deduce that the negative sign before the absolute value will reflect the graph across the x-axis, however, it won't affect the x-coordinate of the vertex.
Furthermore, the value inside the absolute value function is x-a, which translates to a horizontal shift a units to the right. Therefore, the a value directly affects the x-coordinate of the vertex. The + b outside of the absolute value function indicates a vertical shift b units upwards, which influences the y-coordinate of the vertex. Thus, the function's vertex is at the coordinate point (a, b), making the correct answer c) (a, b).