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

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 \( f(x) \) for each \( x \) value and then find \(-f(x)\).

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

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

Now we can fill in the table:

\[
\begin{array}{|c|c|}
\hline
x & -f(x) \\
\hline
0 & -1 \\
1 & 0 \\
2 & -1 \\
\hline
\end{array}
\]

This table represents the reflection over the x-axis of the function \( f(x) = (x - 1)^2 \).