**Which function is a translation of the parent absolute value function?**

A) f(x)= 2x+1

**B) f(x)= ∣x+6∣**

C) f(x)= -4∣1-x∣

D) f(x)= ∣x∣

**Answer:**

**The correct Option is B) f(x) = |x + 6|** represents a translation of the parent **absolute value function,** which in this case is translated into 6 units to the left.

**Explanation: **

The equation of a **translated absolute value function** can be determined using the vertex of the translated graph. **According to algebraic understanding**, an x-direction translation occurs when an addition or subtraction is performed within the function’s argument. Translation refers to moving a graph horizontally without affecting its shape or axis.

Option A stretches the parent absolute function f(x)= 2x+1, instead of translating it. The parent absolute value function in this instance is f(x) = |x|. The function that represents a translation of the parent function must have a comparable form to |x ± d| hence, incorrect. Option B is accurate, as the translation function shifts 6 units to the left.

Option C is the stretching again, therefore not the translation. Therefore, while inaccurate. Option D uses the **parent absolute function,** hence there is no translation. That is why it is inaccurate.

Given the choices:

f(x) = 2x + 1

**f(x) = |x + 6|**

f(x) = -4|x – 1|

f(x) = |x|

Option B) f(x) = |x + 6| represents a 6-unit **translation of the parent function** |x| to the left along the x-axis.

**Also Read: Based on the grapheme representing /sh/, which word is probably from French?**

**FAQs**

**Which function is a translation of the parent?**

A **positive V-shaped graph** with a corner point at (0, 0) represents the function y = | x |. y = | x – 4 | + 3 is a horizontal translation of the parent function four units to the right.

**What is the parent function of all absolute value functions?**

The parent function of an absolute value function is represented by **f(x)=|x|, **which serves as a foundation for figuring out the numerous transformations. The lesson demonstrates how the graph of an absolute value function can be transformed **vertically and horizontally.**

**Which is the graph of the parent absolute value function?**

The parent absolute value function’s graph is v-shaped, having the origin as its vertex. This vertex is also the **lowest point** in the graph.