Question

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

1 unit left and 2 units up
1 unit left and 2 units up

1 unit right and 2 units up
1 unit right and 2 units up

1 unit left and 2 units down

Answer 1

To determine the transformation of the parent function \( f(x) = x^3 \) to the function \( g(x) = (x - 1)^3 - 2 \), we can analyze the modifications made to the function:

1. **Horizontal Shift**: The term \( (x - 1) \) indicates a shift of the graph 1 unit to the right. This is because replacing \( x \) with \( x - 1 \) translates the graph horizontally.

2. **Vertical Shift**: The \( -2 \) outside of the cubic function indicates a shift of the graph 2 units down. This means that every point on the graph of \( f(x) \) is lowered by 2 units.

Combining these transformations, we see that the function \( g(x) \) represents a shift of the parent function \( f(x) = x^3 \) **1 unit right and 2 units down**.

So the correct option is:

**1 unit right and 2 units down**.