The correct answer is the las option (Option D), which is:
D. f(x)=(x+4)^4
The explanation is shown below:
1. The initial function was G(x)=x^4, whose graph shows that the shape has its vertex at 0,0.
2. If the it was shift 4 units to the left, you only has to add a 4 to the function.
3. Therefore, you obtain the the equation of the final shape is:
f(x)=(x+4)^4
As you can see, the answer is the option D.