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The given task asks us to use transformations of the standard cubic function \( f(x) = x^3 \) to graph the function \( h(x) = -(x + 3)^3 \).

Here’s how we can break down the transformations:

### 1. **Start with the basic cubic function**:
   \[
   f(x) = x^3
   \]
   This is the standard cubic function.

### 2. **Horizontal Shift**:
   The expression \( (x + 3) \) indicates a **horizontal shift**. Since it is \( (x + 3) \), the graph of \( f(x) = x^3 \) is shifted **3 units to the left**. The new equation becomes:
   \[
   f(x) = (x + 3)^3
   \]

### 3. **Vertical Reflection**:
   The negative sign in front of the cubic term, \( -(x + 3)^3 \), indicates a **vertical reflection**. This reflects the graph over the x-axis. The graph is now:
   \[
   h(x) = -(x + 3)^3
   \]

### Final Graph:
   The graph of \( h(x) = -(x + 3)^3 \) is obtained by taking the standard cubic graph, shifting it 3 units to the left, and reflecting it over the x-axis.

Would you like further explanation on any specific transformation? 

Here are 5 related questions:
1. How do horizontal and vertical transformations differ in cubic functions?
2. What happens if we add a vertical shift to \( h(x) = -(x + 3)^3 \)?
3. How would the graph change if we had \( h(x) = (x + 3)^3 \) instead of the negative sign?
4. How do you reflect a function across the y-axis versus the x-axis?
5. What is the effect of compressing or stretching the graph of a cubic function?

**Tip:** Always apply horizontal shifts before vertical transformations when analyzing function changes!

Use transformations of the standard cubic function, f(x) = x^3, to graph the function h(x) = -(x + 3)^3.

Learn how to graph the transformation of the standard cubic function f(x) = x^3 into h(x) = -(x + 3)^3. This problem covers key mathematical concepts like horizontal shifts and vertical reflections, suitable for students in Grades 10-12.

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