https://file.aiquickdraw.com/mathbot/file/1727312951315vqfwkf1o.jpg

identify the parent function, identify the transformation represented by the graph, and write an equation

The graph you uploaded represents a **V-shaped** structure, which suggests that the parent function is an **absolute value function**. The general form of an absolute value function is:

\[
y = |x|
\]

### 1. **Parent Function:**
The parent function is:

\[
y = |x|
\]

### 2. **Identifying the Transformation:**
Looking at the graph, we can identify the following transformations:
- The vertex of the graph appears to be shifted to the point \((-6, 0)\) from the origin \((0, 0)\), which means there is a **horizontal shift** of 6 units to the left.
- The slopes of the lines are consistent with the standard slope of \(y = |x|\), so there is no vertical stretch or compression.
  
Thus, the transformation applied is a **horizontal shift 6 units to the left**.

### 3. **Writing the Equation:**
Based on the horizontal shift of 6 units to the left, the transformed equation will be:

\[
y = |x + 6|
\]

### Final Answer:
- **Parent function:** \(y = |x|\)
- **Transformation:** Horizontal shift 6 units to the left.
- **Equation:** \(y = |x + 6|\)

Would you like more details on the graph or the transformation process? Here are some related questions you might find interesting:

1. How can you find the slope of the lines in an absolute value graph?
2. What is the general form of a transformed absolute value function?
3. How does a vertical shift affect the equation of an absolute value graph?
4. How do reflections across the x-axis change the equation of the parent function?
5. What are other types of transformations besides shifts that can apply to absolute value functions?

**Tip:** For absolute value functions, the expression inside the absolute value determines the horizontal shift, while any constants outside affect vertical movement.

Identify the parent function, identify the transformation represented by the graph, and write an equation.

This problem helps students identify the parent function of an absolute value graph, determine the horizontal shift, and write the equation. It demonstrates key algebraic concepts such as absolute value functions and graph transformations. Suitable for students in Grades 8-10.

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