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The problem provided asks for the transformation applied to the graph of \( f(x) = x^3 \) to get the graph of the function \( g(x) = (x + 3)^3 \).

The key observation here is that the transformation is within the argument of the function. Specifically, adding \( +3 \) inside the function \( (x + 3) \) causes a **horizontal shift** to the left by 3 units. 

This happens because adding a constant \( h \) inside a function \( f(x) \) in the form \( f(x + h) \) shifts the graph horizontally by \( -h \) units. Therefore, \( (x + 3)^3 \) shifts the graph 3 units to the left.

Hence, the correct answer is **H. Shift the graph 3 units to the left.**

Let me know if you'd like any further explanation or have questions!

Here are 5 follow-up questions related to this topic:
1. What happens when the function \( f(x) = x^3 \) is transformed into \( g(x) = (x - 2)^3 \)?
2. How would the graph of \( f(x) = x^3 \) change if it were transformed to \( g(x) = x^3 + 5 \)?
3. What is the effect of multiplying the function \( f(x) = x^3 \) by a constant, say \( g(x) = 2x^3 \)?
4. How do vertical shifts differ from horizontal shifts in terms of function transformations?
5. Can you describe the transformation for the function \( f(x) = x^3 \) if it becomes \( g(x) = -x^3 \)?

**Tip**: Always check whether the transformation is happening inside the function (affecting \( x \)) for horizontal shifts, or outside the function (affecting the whole expression) for vertical shifts.

Use transformations of the graph of f(x) = x^3 to determine the graph of the given function. g(x) = (x + 3)^3.

Learn how to transform the graph of f(x) = x^3 to g(x) = (x + 3)^3 using horizontal shifts. Explore the transformation theorem and key concepts for students in Grades 9-12.

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