Answer:
D. The graph of g(x) is the graph of f(x) compressed vertically and then reflected over the x axis.
Explanation:
A function shows the relationship between two or more variables.
If a function y = f(x) is reflected over the x axis, the x coordinate remain unchanged, but the y coordinate is negated. Hence the function y = f(x) becomes y = -f(x).
A function y = f(x) is compressed or stretched vertically by a factor k to give y = kf(x). If 0 < k < 1, the function is vertically compressed whereas if k > 1, the function is vertically stretched.
Given the function f(x) = x², the function is vertically compressed by a factor of 2/3 to form a function f(x)' = (2/3)x². The function is then reflected over the x axis to produce a function g(x) = (-2/3)x²