Question

(1 point)
Part A: When f(x) = (x−1)2
is reflected over the x-axis, the new function is f(x) =

Part B: Complete the table below for the reflection over the x-axis of the function f(x) = (x−1)2

x 0 2 4 6 8
-f(x)

Answer 1

Part A: When the function \( f(x) = (x - 1)^2 \) is reflected over the x-axis, the new function becomes:

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

Part B: To complete the table for the reflection over the x-axis of the function \( f(x) = (x - 1)^2 \), we first need to calculate \( f(x) \) for each x-value in the table. Then, we can find \( -f(x) \).

Let's calculate \( f(x) \) and \( -f(x) \) for each x-value:

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

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

3. For \( x = 4 \):
\[
f(4) = (4 - 1)^2 = 9 \quad \Rightarrow \quad -f(4) = -9
\]

4. For \( x = 6 \):
\[
f(6) = (6 - 1)^2 = 25 \quad \Rightarrow \quad -f(6) = -25
\]

5. For \( x = 8 \):
\[
f(8) = (8 - 1)^2 = 49 \quad \Rightarrow \quad -f(8) = -49
\]

Now we can fill in the table:

| x | 0 | 2 | 4 | 6 | 8 |
|---|---|---|---|---|---|
| -f(x) | -1 | -1 | -9 | -25 | -49 |

So, the completed table for the reflection over the x-axis of the function \( f(x) = (x - 1)^2 \) is:

| x | 0 | 2 | 4 | 6 | 8 |
|---|---|---|---|---|---|
| -f(x) | -1 | -1 | -9 | -25 | -49 |