The graph you provided is a V-shaped graph, which is characteristic of the absolute value function. The parent function for this type of graph is:

$f(x) = |x|$

Identifying the Transformation:

To identify the transformation, we compare the given graph to the parent function $f(x) = |x|$, which normally has a vertex at $(0, 0)$.

1. Horizontal shift: The vertex of the given graph is located at $(-6, 0)$, so the graph has been shifted 6 units to the left.

2. Vertical stretch: The graph appears to maintain the same slope as the parent function. This indicates no vertical stretch or compression.

Thus, the function that represents the transformation is:

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

Summary:

• Parent function: $f(x) = |x|$
• Transformation: Shifted 6 units to the left, no vertical or horizontal stretch/compression.

Would you like more details or have any further questions?

Here are 5 related questions to expand your understanding:

1. How would the graph change if the absolute value function was $f(x) = |x - 2|$?
2. What transformation occurs if you multiply the absolute value function by a constant, such as $2|x|$?
3. How do horizontal shifts affect the domain of an absolute value function?
4. What is the effect of reflecting the absolute value function across the x-axis (e.g., $f(x) = -|x|$)?
5. How do you determine the range of a transformed absolute value function?

Tip: For absolute value functions, the vertex represents the minimum (or maximum, if reflected) point, and transformations like shifts and stretches directly affect its position and shape.