Final answer:
The parent function of all absolute value functions is f(x) = |x|, the simplest form that represents the properties of all absolute value functions, making 'B. f(x) = |x|' the correct answer.
Step-by-step explanation:
The parent function of all absolute value functions is f(x) = |x|. This is the simplest form of an absolute value function and represents the basic shape and properties that all absolute value functions have, regardless of transformations such as stretching, compressing, translating, or reflecting.
- Absolute value functions are always non-negative.
- The graph of an absolute value function makes a 'V' shape.
- The vertex of this 'V' at the origin (0,0) for the parent function f(x) = |x|.
All other absolute value functions can be considered transformations of this parent function. For example, f(x) = 2|x| is a vertical stretch of the parent function by a factor of 2. Therefore, the correct answer to the question 'Which of the following is the parent function of all absolute value functions?' is B. f(x) = |x|.