Final answer:
The function f(x)=-x²-2 is obtained by reflecting the graph of y=x² about the x-axis and translating it downward by 2 units.
Step-by-step explanation:
The function f(x)=-x²-2 is obtained by taking the common function y=x² and applying two transformations: a reflection about the x-axis and a translation downward by 2 units.
First, the negative sign in front of x² reflects the graph of y=x² about the x-axis. This means that every point on the graph, such as (1, 1), is reflected to (-1, 1).
Next, the constant term -2 shifts the entire graph downward by 2 units. This means that every y-coordinate is decreased by 2, resulting in a new graph that is lower than the graph of y=x².