Final answer:
Option b) f(x) = |x + 6| is the function that represents a translation of the parent absolute value function, which in this case is translated 6 units to the left.
Step-by-step explanation:
The question asks which function is a translation of the parent absolute value function. Based on algebraic knowledge, a translation in the x-direction occurs when there is an addition or subtraction inside the function's argument. If f(x) is the parent function, a translation to the right by d units would result in the function f(x - d), and a translation to the left by d units would yield f(x + d). In this case, the parent absolute value function is f(x) = |x|. Thus, the function which represents a translation of the parent function would have to have a form similar to |x ± d|.
Given the choices:
f(x) = 2x + 1
f(x) = |x + 6|
f(x) = |x|
f(x) = -4|x - 1|
Option b) f(x) = |x + 6| shows a translation of the parent function |x| to the left by 6 units on the x-axis.