Question

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 of the function \( f(x) = (x - 1)^2 \) over the x-axis, we first need to compute \( f(x) \) for the given \( x \) values. The reflection over the x-axis is given by \(-f(x)\).

Let's calculate \( f(x) \) and then \(-f(x)\):

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

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

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

Now, we can create the table:

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

So, the table for the reflection over the x-axis of the function is as follows:

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