The given graph shows a transformation of the function $f(x) = |x|$. The original absolute value function has its vertex at $(0, 0)$ and opens upward with a slope of 1 on both sides.

Analyzing the Transformation:

From the graph, we observe the following:

1. Vertex Shift: The vertex of the new function $g(x)$ is located at $(-2, 0)$, indicating a horizontal shift to the left by 2 units.
2. Vertical Stretch: The graph opens upward and appears narrower than the basic absolute value function, indicating a vertical stretch. The slope of the right side of the V is 2 instead of 1, so the function has been vertically stretched by a factor of 2.

Writing the Transformation:

The general form of the transformation for an absolute value function is: $g(x) = a |x - h| + k$ Where:

• $a$ is the vertical stretch or compression factor.
• $h$ represents the horizontal shift (right or left).
• $k$ represents the vertical shift (up or down).

In this case: