Final answer:
The graph of g(x) = |x| + 9 is the graph of f(x) = |x| shifted 9 units up on the y-axis.
Step-by-step explanation:
The graph of g(x) = |x| + 9 is the graph of f(x) = |x| shifted 9 units up on the y-axis. This means that every point on the graph of f(x) has been moved 9 units upward to create the graph of g(x).
For example, if we take the point (2, 2) on the graph of f(x), the corresponding point on the graph of g(x) would be (2, 11) since we have moved 9 units up on the y-axis.
In summary, adding a constant term to the absolute value function shifts the graph vertically by that amount.
Learn more about Translations of Absolute Value Functions