The transformation of $f(x) = x^3$ represented by $g(x) = (x - 5)^3$ is a horizontal translation to the right by 5 units.

Here’s how it works:

1. Base function: $f(x) = x^3$ is a cubic function centered at the origin (0,0). Its graph is symmetric about the origin.

2. Horizontal translation: In $g(x) = (x - 5)^3$, the expression $x - 5$ inside the cubic function indicates a shift. Specifically, subtracting 5 from $x$ translates the graph of $f(x)$ horizontally by 5 units to the right.

In summary:

• The transformation moves the graph of $f(x) = x^3$ to the right by 5 units, but the shape and orientation of the graph (its cubic nature) remain unchanged.

Would you like more details, or have any other questions?

Here are 5 related questions for deeper understanding:

1. How would the graph of $f(x) = x^3$ change if the transformation were $g(x) = (x + 5)^3$?
2. What is the effect of a vertical translation on $f(x) = x^3$?
3. How does a reflection across the y-axis affect the graph of $f(x) = x^3$?
4. What would be the result of applying a vertical stretch to $f(x) = x^3$?
5. Can you combine a