Question

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
-f(x)

Answer 1

To reflect the function \( f(x) = (x - 1)^2 \) over the x-axis, we calculate \(-f(x)\) for each value of \(x\).

1. First, compute \( f(x) \) for the values of \( x \) given in the table:
- 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. Next, calculate \(-f(x)\) for each \(x\):
- 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 \( x = 8 \):
\[ -f(8) = -49 \]

Now, combining the results, we fill in the table:

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

The completed table is:

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