The range is "(-∞, -6]," the domain is "(-∞, ∞)," and the graph is a function of x.
A. For the quadratic function "y = -x^2 - 6," let's analyze the range, which is the set of all possible y-values. Since the coefficient of the "x^2" term is negative, the parabola opens downward. This means that the y-values extend downward indefinitely, and there is no upper bound. Therefore, the range is "(-∞, -6]" in interval notation.
B. The domain of a quadratic function is the set of all possible x-values. In this case, since there are no restrictions on x, the domain is all real numbers. Therefore, the domain is "(-∞, ∞)" in interval notation.
C. To determine if the graph represents a function of x, we apply the vertical line test. If any vertical line intersects the graph at more than one point, the graph is not a function. In the case of a downward-opening parabola, like "y = -x^2 - 6," no vertical line will intersect the graph at more than one point. Therefore, the graph is a function of x.
In summary, for the quadratic function "y = -x^2 - 6," the range is "(-∞, -6]," the domain is "(-∞, ∞)," and the graph is a function of x.