Final answer:
The function g(x) is obtained by translating the function f(x) = |x| first 9 units left horizontally and then 5 units down vertically.
Step-by-step explanation:
The functions f(x) = |x| and g(x) = |x + 9| - 5 can be considered as transformations of each other. To describe the transformation from f(x) to g(x), consider that g(x) has two modifications applied to f(x): a horizontal translation and a vertical translation.
Firstly, the term |x + 9| indicates a horizontal shift. Since it is x plus 9, this is a shift 9 units to the left (negative direction). In general, f(x - d) would translate the function d units to the right, but here we have f(x + 9), so it's 9 units to the left.
Secondly, the -5 at the end of g(x) tells us there is also a vertical translation. The function f(x) is shifted downwards by 5 units.
Therefore, the transformation involves a horizontal shift of 9 units to the left and a vertical shift of 5 units down.