Final answer:
The equation suggests a transformation applied to the x-values of function f, indicating a horizontal transformation. The function has been shifted horizontally to the right by 4 units, so the correct answer is a horizontal transformation of function f 4 units right.
Step-by-step explanation:
Given the function equation (x - 4) * g(2) = (x + 4), we are looking to describe the transformation of function g compared to function f. This equation can be interpreted as a transformation applied to the x-values of the graph of function f, where function g at 2 is involved in the transformation from f to g.
If we distribute g(2) on the left side, we get g(2)x - 4g(2) = x + 4. If we assume g(2) is not equal to zero, this would imply that x is being transformed by a shift. To isolate x on one side, we would divide by g(2), leading to an equation that looks like x = (x + 4)/g(2) + 4, which indicates a horizontal shift. Since x - 4 changes to x + 4 when transformed to g, it means that the function has been shifted horizontally to the right by 4 units. Therefore, the correct description represents a horizontal transformation of function f 4 units right.