To write the function rule for $g(x)$, we need to determine how the graph of $f(x) = x^2$ has been translated.

Steps to Identify the Transformation:

1. Vertical Shift: If the graph is moved up by $k$ units, the new function is $g(x) = x^2 + k$. If moved down, it is $g(x) = x^2 - k$.
2. Horizontal Shift: If the graph is moved right by $h$ units, the function becomes $g(x) = (x - h)^2$. If moved left, it becomes $g(x) = (x + h)^2$.
3. Reflections & Stretches: If the graph is flipped downward, the function has a negative sign: $g(x) = -x^2$. If it is stretched or compressed, a coefficient $a$ is added: $g(x) = a(x - h)^2 + k$.

Solution:

Please upload the graph so I can analyze the specific transformation and provide the exact function rule for $g(x)$.

Would you like an example of how different translations affect a function?
Here are five related questions:

1. How does shifting a function horizontally affect its equation?
2. What does the coefficient $a$ do in $g(x) = a(x - h)^2 + k$?
3. How do you reflect a function across the x-axis or y-axis?
4. What is the vertex form of a quadratic function?
5. How can you determine the equation of a parabola given its vertex?

Tip: The vertex of a quadratic function in the form $g(x) = a(x - h)^2 + k$ is at $(h, k)$.