The correct option is:
B) g(2) = - (4(2) - 4)3 - 9
Step-by-step explanation:
According to the given transformations, we start with the function f(x), which is given by:
f(a) = (2 - 4a) + 3
The transformations applied to f(x) are:
1. Horizontal shrink by a factor of f and a
2. Translation 6 units up
3. Reflection in the x-axis
To apply these transformations to f(a), we substitute a with 2 and follow the order of operations:
1. Horizontal shrink by a factor of f and a:
(2 - 4a) becomes (2 - 4(2)) = (2 - 8) = -6
2. Translation 6 units up:
-6 + 6 = 0
3. Reflection in the x-axis:
The reflection changes the sign of the function, so -0 becomes 0.
Therefore, g(2) = 0.
Among the given options, option B) correctly represents this transformation.