To create a table reflecting the function \( f(x) = (x - 1)^2 \) over the x-axis, we first need to calculate the values of \( f(x) \) for the provided \( x \) values and then take the negative of those values to get \(-f(x)\).
- Calculate \( f(x) = (x - 1)^2 \)
- Calculate \(-f(x)\)
Now let's compute these values for \( x = 0, 1, 2 \).
Step 1: Calculate \( f(x) \)
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For \( x = 0 \): \[ f(0) = (0 - 1)^2 = 1 \]
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For \( x = 1 \): \[ f(1) = (1 - 1)^2 = 0 \]
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For \( x = 2 \): \[ f(2) = (2 - 1)^2 = 1 \]
Step 2: Calculate \(-f(x)\)
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For \( x = 0 \): \[ -f(0) = -1 \]
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For \( x = 1 \): \[ -f(1) = 0 \]
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For \( x = 2 \): \[ -f(2) = -1 \]
Final Table
| \( x \) | 0 | 1 | 2 | |:---------:|:----:|:----:|:----:| | \( -f(x) \) | -1 | 0 | -1 |
This table represents the values of the reflection of the function \( f(x) = (x - 1)^2 \) over the x-axis at the specified x-values.