Question

Part A: When f(x) = (x−1)2
is reflected over the x-axis, the new function is f(x) =

Part B: Complete the table below for the reflection over the x-axis of the function f(x) = (x−1)2

x 0 2 4 6 8

Answer 1

Part A: When the function \( f(x) = (x-1)^2 \) is reflected over the x-axis, the new function becomes \( f(x) = -(x-1)^2 \).

Part B: To complete the table for the reflection over the x-axis of the function \( f(x) = (x-1)^2 \), we first calculate the original values of \( f(x) \) for the given \( x \) values and then negate those values for the reflected function.

1. Calculate \( f(x) \) for the original function:
- For \( x = 0 \): \( f(0) = (0-1)^2 = 1 \)
- For \( x = 2 \): \( f(2) = (2-1)^2 = 1 \)
- For \( x = 4 \): \( f(4) = (4-1)^2 = 9 \)
- For \( x = 6 \): \( f(6) = (6-1)^2 = 25 \)
- For \( x = 8 \): \( f(8) = (8-1)^2 = 49 \)

2. Now reflect over the x-axis by negating these values:
- For \( x = 0 \): \( f(0) = -1 \)
- For \( x = 2 \): \( f(2) = -1 \)
- For \( x = 4 \): \( f(4) = -9 \)
- For \( x = 6 \): \( f(6) = -25 \)
- For \( x = 8 \): \( f(8) = -49 \)

The completed table is as follows:

| x | 0 | 2 | 4 | 6 | 8 |
|-----|------|------|------|------|------|
| f(x)| -1 | -1 | -9 | -25 | -49 |