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