Answer: The transformation of the function f(x) = x^2 represented by g(x) = -2x^2 involves a reflection over the x-axis and a vertical compression by a factor of 2.
1. Reflection over the x-axis: When the coefficient of x^2 in g(x) is negative (-2 in this case), it reflects the graph of f(x) over the x-axis. This means that any points on the graph of f(x) will be mirrored across the x-axis in the graph of g(x).
2. Vertical compression by a factor of 2: The absolute value of the coefficient of x^2 in g(x) (2 in this case) represents the vertical compression or stretching factor. In this transformation, the graph of f(x) is compressed vertically by a factor of 2, making it narrower compared to the original function.
Combining these transformations, the function g(x) = -2x^2 will have a graph that is a reflection of the graph of f(x) = x^2 across the x-axis and vertically compressed by a factor of 2.
Step-by-step explanation:
