Question

given the parent function f(x)=x^3, the function g(x)=(x-1)^3-2 is the result of a shift off f(x)
1 unit right and 2 units up
1unit left and 2 units down
1 unit right and 2 units down
1 unit left and 2 units up

Answer 1

To analyze the transformation of the parent function \( f(x) = x^3 \) to the function \( g(x) = (x-1)^3 - 2 \), we need to understand how shifts work.

1. **Horizontal Shift**: The expression \( (x - 1) \) indicates a horizontal shift. Specifically, \( (x - 1) \) shifts the graph **1 unit to the right**.

2. **Vertical Shift**: The expression \(-2\) outside the cubic function indicates a vertical shift. Specifically, subtracting 2 shifts the graph **down by 2 units**.

Combining these two shifts, we can conclude that the function \( g(x) = (x-1)^3 - 2 \) is the result of a shift of \( f(x) = x^3 \) **1 unit right** and **2 units down**.

So, the correct answer is:
**1 unit right and 2 units down.**