From the graph you provided, we can observe that the function $g(x)$ is a transformation of the absolute value function $f(x) = |x|$.

Analysis of the transformation:

1. Vertical stretch/shrink: The slope of the lines forming the "V" shape in $g(x)$ is 2, as the graph rises by 2 units for every 1 unit horizontally. This indicates that there is a vertical stretch by a factor of 2. Thus, $a = 2$.

2. Horizontal shift: The vertex of the original $f(x) = |x|$ is at the origin (0, 0). However, in $g(x)$, the vertex has shifted to $(-2, 0)$. This indicates a horizontal shift to the left by 2 units. Thus, $h = -2$.

3. Vertical shift: The graph does not appear to have shifted vertically, as the vertex remains on the x-axis. Therefore, $k = 0$.

Conclusion:

The function rule for $g(x)$ is in the form: $g(x) = a |x - h| + k$ Substituting $a = 2$, $h = -2$, and $k = 0$, we get: $g(x) = 2 |x + 2|$

This is the function rule for $g(x)$.

Would you like more details or have any questions?

Here are some related questions to explore:

1. How do you determine the vertex of an absolute value function from its equation?
2. What is the significance of the parameter $a$ in an absolute value transformation?
3. How does the graph change when the value of $h$ is positive versus negative?
4. What happens if the value of $k$ is non-zero in the absolute value transformation?
5. How would the graph look if $a$ were a fraction instead of an integer?

Tip: When analyzing transformations, always start by identifying the vertex, then check for any stretching, compressions, or shifts.