To determine the transformation from \( f(x) \) to \( g(x) \), we can analyze the given values in both tables.
Examining the values for \( f(x) \):
- \( f(-1) = 2 \)
- \( f(0) = -1 \)
- \( f(1) = -2 \)
- \( f(2) = -1 \)
- \( f(3) = 2 \)
Now looking at \( g(x) \):
- \( g(-12) = 2 \)
- \( g(0) = -1 \)
- \( g(12) = -2 \)
- \( g(1) = -1 \)
- \( g(32) = 2 \)
We can see that the \( y \)-values of \( g(x) \) match \( f(x) \) inversely around the x-axis when considering the corresponding \( x \)-values.
Next, let's analyze the relationship in terms of \( x \):
- The \( x \)-values are scaled by a factor of 12: \( -12, 0, 12, 1, 32 \) does not maintain the symmetry.
- Noticing that while \( f(-1) = 2 \) matches \( g(-12) = 2 \) and \( f(3) = 2 \) matches \( g(32) = 2 \), the coordinates appear transformed substantially.
But observing further:
- The x-values of \( g(x) \) are adjusted. If we check y-values, \( g(-12) = 2 \) matches \( f(-1) \) with increment in x-area.
- \( g(0) = -1 \) matches \( f(0) = -1 \).
- \( g(12) = -2 \) matches \( f(1) = -2 \).
Thus it appears that the \( x \)-values of the corresponding function \( g(x) \) are actually reflections of the \( f(x) \) values due to the steep change across the middle which outlines a reflection horizontally.
To summarize: The transformation applied to obtain \( g(x) \) from \( f(x) \) appears to be a horizontal dilation by a scale factor of 12, as every \( x \) in \( g(x) \) represents \( f \) evaluated at different scaled intervals \( (every 12 units) \).
Given the provided responses, the closest and most fitting transformation is Horizontal dilation by a scale factor of 2.