Final answer:
The graph of g(x) is the graph of f(x) shifted up 9 units, because adding a constant to a function results in a vertical translation of the graph by that amount.
Step-by-step explanation:
To determine how the graph of g(x) might differ from that of f(x) when given g(x) = f(x) + 9, we must understand the effect of adding a number to the function. In algebra, when we add a constant to a function, it translates the graph vertically. Since g(x) is f(x) plus 9, the entire graph of f(x) is shifted 9 units upward. Thus, every point on the graph of f(x) will now be 9 units higher on the g(x) graph.
It is essential to understand that adding or subtracting a number to/from the entire function (outside the function itself) does not move the graph left or right but up or down. Therefore, the correct answer is that the graph of g(x) is the graph of f(x) shifted up 9 units.