To write the function rule for \( g(x) \) as a translation of \( f(x) = x^2 \), we can use the vertex form of a quadratic function, which is given by:
\[ g(x) = a(x - h)^2 + k \]
Where:
- \( a \) represents the vertical stretch (or compression) and reflects the parabola.
- \( (h, k) \) is the vertex of the parabola, which represents the translation of the function.
To fill in the rules for \( g(x) \), I would need to see the graphs or have a description of the transformations that have been applied to the function \( f(x) = x^2 \).
If you provide details about the transformations (such as shifts left/right, up/down, reflections, and stretches), I can help create specific equations for \( g(x) \).