Question

Identify the function that represents a translation of the parent absolute value function y = |x|.

A) f(x) = 2|x|
B) f(x) = |x + 6|
C) f(x) = |x]|
D) f(x) = -4|x|

Answer 1

The function that represents a translation of the parent absolute value function y = |x| is B) f(x) = |x + 6|, which shifts the parent function 6 units to the left on the x-axis.

Step-by-step explanation:

The student's question asks to identify the function that represents a translation of the parent absolute value function y = |x|. When analyzing the given functions, we are looking for an expression that shifts the graph of the parent function along the x-axis.

According to the principles of function translation, the function f(x) = |x + d| is the parent absolute value function translated d units in the negative x-direction. Conversely, the function f(x) = |x - d| is translated d units in the positive x-direction. Therefore, the correct answer is B) f(x) = |x + 6|, which represents the parent function translated 6 units to the left.