Question

Create a table for the reflection over the x-axis of the function f(x)=(x−1)2.(2 points)
x 0 1 2
−f(x)

Answer 1

To create a table for the reflection over the x-axis of the function \( f(x) = (x - 1)^2 \), we need to calculate \( -f(x) \) for the given \( x \) values. Below are the calculations and resulting table:

1. Calculate \( f(x) \):
- For \( x = 0 \):
\[ f(0) = (0 - 1)^2 = 1 \]
- For \( x = 1 \):
\[ f(1) = (1 - 1)^2 = 0 \]
- For \( x = 2 \):
\[ f(2) = (2 - 1)^2 = 1 \]

2. Now calculate \( -f(x) \):
- For \( x = 0 \):
\[ -f(0) = -1 \]
- For \( x = 1 \):
\[ -f(1) = 0 \]
- For \( x = 2 \):
\[ -f(2) = -1 \]

Now we can present the values in a table:

| \( x \) | \( f(x) \) | \( -f(x) \) |
|---------|-------------|---------------|
| 0 | 1 | -1 |
| 1 | 0 | 0 |
| 2 | 1 | -1 |

Thus, the completed table is as shown above.