Final answer:
The function g(x) is a vertical translation of the function f(x) by 2 units up, as the slope remains unchanged and the y-intercept increases by 2. The correct answer is option B. g(x) is a vertical translation 2 units down.
Step-by-step explanation:
The function g(x) = 2x + 8 is a translation of the function f(x) = 2x + 6. When comparing these two functions, it's clear that they have the same slope, which indicates that there is no horizontal translations involved. The only difference between g(x) and f(x) is the constant term, which has increased from 6 to 8 in g(x). Therefore, the translation is vertical. The increase by 2 units in the constant term results in a vertical translation of the graph of f(x) by 2 units upwards.
To confirm this, we look at the general form of a linear function, y = mx + b, where m represents the slope and b represents the y-intercept. Since the slope remains unchanged, but the y-intercept has increased by 2, it is indeed a vertical shift.
Therefore, the correct answer to the question is: B. g(x) is a vertical translation 2 units up.