Question

What does the transformation f(x)↦f(x–8)–1 do to the graph of f(x)?

translates it 8 units left and 1 unit up

translates it 8 units right 1 unit down

translates it 8 units left 1 unit down

translates it 8 units right 1 unit up

Answer 1

To analyze the transformation \( f(x) \mapsto f(x - 8) - 1 \), we can break it down into two parts:

1. **Horizontal Translation**: The expression \( f(x - 8) \) indicates a horizontal shift. Specifically, replacing \( x \) with \( x - 8 \) translates the graph of \( f(x) \) **8 units to the right**.

2. **Vertical Shift**: The expression \( -1 \) at the end indicates a vertical shift. In this case, it shifts the graph **1 unit down**.

Combining these two transformations, the overall effect of the transformation \( f(x) \mapsto f(x - 8) - 1 \) is that it translates the graph:

- **8 units to the right**
- **1 unit down**

Therefore, the correct choice among the options provided is:

**translates it 8 units right 1 unit down**.