Question

Create a table for the reflection over the x-axis of the function f(x) = (x - 1) ^ 2
X 0 1 2
-f (x)

Answer 1

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 \(-f(x)\).

1. Calculate \( f(x) = (x - 1)^2 \)
2. Calculate \(-f(x)\)

Now let's compute these values for \( x = 0, 1, 2 \).

### Step 1: Calculate \( f(x) \)

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

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

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

### Step 2: Calculate \(-f(x)\)

- For \( x = 0 \):
\[
-f(0) = -1
\]

- For \( x = 1 \):
\[
-f(1) = 0
\]

- 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.