Final answer:
The graph of the function f(x) = -(X + 8)^2 - 1 is decreasing over the interval (-8, ∞), which corresponds to option a. (-8, ∞)
Step-by-step explanation:
The question asks over what interval the graph of the function f(x) = -(X + 8)² − 1 is decreasing. To determine the intervals of increase or decrease, we can look at the vertex of the parabola represented by the function. Because the coefficient of the x² term is negative, the parabola opens downwards. The vertex form of the equation is given by the expression inside the square, which tells us the vertex is at (-8, -1).
Since the parabola is symmetric about the vertex and opens downwards, it will be decreasing to the right of the vertex. Thus, the graph of the function is decreasing over the interval (-8, ∞). This corresponds to option a. (-8, ∞).