Short Answer 
The process involves understanding the parent function, which is the absolute value function f(x) = |x|. The translation results in the function g(x) = |x| – 4, representing a downward shift of the graph by 4 units. Consequently, g(x) appears consistently 4 units below f(x) in its visual representation.
Step 1: Understand the Parent Function
The parent function in this case is defined as f(x) = |x|, which represents the absolute value function. This function is characterized by a V-shaped graph that opens upwards. It serves as the basis for the translation we will perform in the next steps.
Step 2: Identify the Translation
The translated function, g(x), is derived from the parent function by shifting it downwards. Specifically, it can be expressed as g(x) = |x| – 4. This means that every point on the graph of f(x) is moved 4 units down to form the graph of g(x).
Step 3: Visualize the Graph Translation
To visualize the transformation, note that the graph of g(x) will be consistently 4 units below the graph of f(x). This allows you to see how the two functions relate to each other. In essence, the graph of g(x) is simply a vertical shift of the graph of f(x) downward.