Final answer:
The graph of f(x) = 2x needs to be shifted horizontally to the left by 8 units to obtain the graph of g(x) = 2(x + 8) due to the addition of 8 inside the parentheses with the x variable.
Step-by-step explanation:
The graph of the function f(x) = 2x must be shifted to produce the graph of g(x) = 2(x + 8). Comparing f(x) with g(x), we notice that the x in f(x) has been replaced by (x + 8). This substitution implies that the graph of g(x) should shift horizontally to the left side of the coordinate system by 8 units because x has effectively been replaced with a new variable (x shifted to the left). According to the reference given, the direction of the motion to the left has a minus sign, which supports the concept that the graph moves left when dealing with positive numbers being subtracted inside the function's parenthesis.