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!