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)

Answer 1

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 \( x \)

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

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

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

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

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

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

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