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.