To create a reflection over the x-axis for the function \( f(x) = (x - 1)^2 \), we need to calculate the values of \( -f(x) \). Here, \( -f(x) \) means we will take the negative of the output of the function \( f(x) \).
Let's calculate \( f(x) \) at the given values of \( x \), and then find \( -f(x) \).
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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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Calculate \( -f(x) \):
- For \( x = 0 \): \[ -f(0) = -1 \]
- For \( x = 1 \): \[ -f(1) = -0 = 0 \]
- For \( x = 2 \): \[ -f(2) = -1 \]
Now we can summarize this data in a table format.
| \( x \) | \( -f(x) \) | |---------|-------------| | 0 | -1 | | 1 | 0 | | 2 | -1 |
This table shows the reflection of the function \( f(x) = (x - 1)^2 \) over the x-axis.
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