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)


Remaining Attempts : 3
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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 values of \( x \).

First, let’s calculate \( f(x) \) for each value of \( x \):

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

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

3. For \( x = 2 \):
\[
f(2) = (2 - 1)^2 = 1^2 = 1 \quad \Rightarrow -f(2) = -1
\]

Now we can create the table:

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

So the final table for the reflection over the x-axis of the function \( f(x) = (x-1)^2 \) is given above.