Final answer:
The absolute value function that fits the given description is f(x) = -2|x - 3| - 5, which has a vertex at (3, -5), opens downward, and is vertically stretched by a factor of 2.
Step-by-step explanation:
The question involves writing an absolute value function that has been transformed to have a vertex at (3,-5), opens down, and is stretched by a factor of 2.
The general form of an absolute value function is f(x) = a|bx - h| + k, where (h,k) is the vertex and a controls the vertical stretch and direction of the opening.
Since the vertex is at (3, -5) and the function opens down and is stretched by a factor of 2, the value of a will be -2 (opening down indicates a negative value, and the stretch factor is 2).
There is no horizontal stretch or compression, therefore b remains 1.
Thus, the function will be f(x) = -2|x - 3| - 5.