To create a table for the reflection over the x-axis of the function \( f(x) = (x-1)^2 \), we first need to calculate the values of \( f(x) \) at the given \( x \) values: 0, 1, and 2.
Then, we will take the negative of those values to represent the reflection over the x-axis, resulting in \( -f(x) \).
Step 1: Calculate \( f(x) \) for each \( x \)
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For \( x = 0 \): \[ f(0) = (0 - 1)^2 = (-1)^2 = 1 \]
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For \( x = 1 \): \[ f(1) = (1 - 1)^2 = 0^2 = 0 \]
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For \( x = 2 \): \[ f(2) = (2 - 1)^2 = 1^2 = 1 \]
Step 2: Calculate \( -f(x) \)
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For \( x = 0 \): \[ -f(0) = -1 \]
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For \( x = 1 \): \[ -f(1) = -0 = 0 \]
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For \( x = 2 \): \[ -f(2) = -1 \]
Step 3: Create the table
Now we can construct the table:
| \( x \) | \( -f(x) \) | |---------|-------------| | 0 | -1 | | 1 | 0 | | 2 | -1 |
This table represents the reflection over the x-axis of the function \( f(x) = (x-1)^2 \).