Final answer:
The function ƒ(x) that results from translating the function g(x) = 0.75(x - 4³ - 2) thirteen units to the left and seven units downward is ƒ(x) = 0.75(x - 13) - 7.
Step-by-step explanation:
To find the function ƒ(x) that results from translating the function g(x) = 0.75(x - 4³ - 2) thirteen units to the left and seven units downward, we can use the general equation for translating a function.
The general equation for translating a function g(x) is: ƒ(x) = a*g(x - h) + k, where a represents vertical stretching/shrinking, h represents horizontal translation, and k represents vertical translation.
In this case, the function g(x) has a = 0.75, h = 13, and k = -7. So the function ƒ(x) can be written as: ƒ(x) = 0.75(x - 13) - 7.