Final answer:
The graph of f(x) transforms to g(x) through a vertical compression, as the coefficient of x goes from -8 to -2, and a vertical translation downward by 3 units, as the constant term changes from +4 to +1. The correct answer is A) Vertical compression and vertical translation.
Step-by-step explanation:
The transformation that converts the graph of f(x) = -8|x| + 4 to g(x) = -2|x| + 1 involves comparing the coefficients of x and the constant terms in both functions. Looking at the coefficients of |x|, we can see that the coefficient in function f(x) is -8, while in function g(x) it is -2. This indicates that the graph of f(x) is subjected to a vertical compression, as the absolute value of the coefficient is reduced from 8 to 2.
Next, by comparing the constant terms, we observe that the f(x) has a constant term of +4, while g(x) has a constant term of +1. This signifies a vertical translation downward by 3 units since the graph has shifted from being 4 units above the x-axis to being just 1 unit above.
Therefore, the correct answer is A) Vertical compression and vertical translation.