Given the function $f(x) = x^3$, we need to apply two transformations:

1. Shift the function to the right by 7 units.
   To achieve this, we replace $x$ with $(x - 7)$. So the transformed function becomes:
   $f(x - 7) = (x - 7)^3$

2. Flip the function over the x-axis.
   To flip a function over the x-axis, we multiply the entire function by $-1$. Thus, the final transformation becomes:
   $-f(x - 7) = -(x - 7)^3$

So, the transformed function is: $g(x) = -(x - 7)^3$

Do you want more details or have any questions?

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Here are 5 related questions:

1. What happens when a function is shifted left instead of right?
2. How does a vertical flip affect the graph of different types of functions?
3. What is the effect of flipping a function over the y-axis?
4. How would the graph of $f(x) = x^3$ change if we reflected it over both the x-axis and y-axis?
5. How does horizontal scaling affect transformations?

Tip: For horizontal shifts, replacing $x$ with $(x - h)$ moves the graph right by $h$ units. Replacing it with $(x + h)$ moves the graph left.