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
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page 8 of 9

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 evaluate \( f(x) \) for the given \( x \) values and then take the negative values of those outputs, since reflecting a function over the x-axis involves negating the function's y-values.

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

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

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

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

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

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

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

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

**Final Table:**

| x | 0 | 1 | 2 |
|---|------|-----|------|
| -f(x) | -1 | 0 | -1 |

This table shows the values of \( -f(x) \) for the given \( x \)-values, representing the reflection of the function \( f(x) = (x - 1)^2 \) over the x-axis.