Final answer:
The function f(x+8)-1 represents a horizontal shift left 8 units and a vertical shift down 1 unit, corresponding to option B.
Step-by-step explanation:
The student is asking about the transformation of the function f(x+8)-1. When we have a function of the form f(x+h), this indicates a horizontal shift of the graph of the function f(x). If h is positive, the shift is horizontally to the left side of the coordinate system by h units. If h is negative, the shift is horizontally to the right side of the coordinate system by the absolute value of h units. On the other hand, when we subtract a number from the whole function like f(x) - k, it indicates a vertical shift of the graph. If k is positive, the shift is vertically downward in the coordinate system by k units. If k is negative, the shift is vertically upward in the coordinate system by the absolute value of k units.
In the function f(x+8)-1, the +8 inside the brackets indicates a horizontal shift by 8 units, and since it's positive, the shift is to the left. The -1 outside the function indicates a vertical shift by 1 unit, and since it's negative, the shift is downward. Therefore, option B is correct: Horizontal shift left 8 units and vertical shift down 1 unit.