Describe the transformation of f represented by g.
f(x) = x3, g (x) = (x - 5)3

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

Describe the transformation of f represented by g. f(x) = x^3, g(x) = (x - 5)^3

Understand how the cubic function f(x) = x^3 transforms into g(x) = (x - 5)^3. This problem demonstrates a horizontal translation of the graph by 5 units to the right. Suitable for Grades 9-11, covering key concepts in algebra and graph transformations.

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