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The given problem asks for the expression for \( g(x) \), where the function \( f(x) = x^2 \) is provided.

The graph shows the transformation of the basic function \( f(x) = x^2 \) into \( g(x) \). Based on the graph, we can see that \( g(x) \) is a reflection of \( f(x) = x^2 \) over the x-axis and shifted to the left by 2 units.

This indicates two transformations:
1. A horizontal shift of 2 units to the left: \( f(x+2) \).
2. A reflection over the x-axis: \( -f(x+2) \).

Thus, the expression for \( g(x) \) is:

\[
g(x) = -(x + 2)^2
\]

Let me know if you'd like further clarification or additional steps!

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### Related Questions:
1. What are other types of transformations that can be applied to functions?
2. How do you determine whether a graph is reflected across the x-axis or y-axis?
3. What is the general form of a quadratic function with vertical and horizontal shifts?
4. How would you write the equation for a parabola shifted to the right instead of the left?
5. What are the effects of stretching or compressing a quadratic function?

**Tip:** Always verify transformations by plugging in key points (like the vertex) and checking how they move on the graph.

The function f(x) is defined by f(x) = x^2. Write down the expression for g(x), based on the provided graph.

Discover how to determine the expression for g(x) based on the graph of the quadratic function f(x) = x^2, which has undergone transformations. This example includes a horizontal shift and reflection over the x-axis, perfect for students in Grades 9-11.

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