Question

Create a table for the reflection about the origin of the function
f(x) = (x + 2)} + 1.
Hint: First create a table of values for f (x) evaluated at x = 0, x = -1.,
and x = -2.

x - 0, 1, 2
-f(-x) - ?, ?, ?

Dont calculate just say the three points for -f(-x) please

Answer 1

To reflect on the function \( f(x) = (x + 2) + 1 \), we will evaluate the transformation \( -f(-x) \). First, we will find the points for \( f(x) \) at \( x = 0, -1, \) and \( -2 \). Then we will determine the corresponding points for \( -f(-x) \).

1. **Calculate \( f(x) \)**:
- \( f(0) = (0 + 2) + 1 = 3 \)
- \( f(-1) = (-1 + 2) + 1 = 2 \)
- \( f(-2) = (-2 + 2) + 1 = 1 \)

2. **Values of \( f(x) \)**:
- For \( x = 0 \): \( f(0) = 3 \)
- For \( x = -1 \): \( f(-1) = 2 \)
- For \( x = -2 \): \( f(-2) = 1 \)

3. **Now, evaluate \( -f(-x) \)**:
- For \( -x = 0 \) (which means \( x = 0 \)): \( -f(-0) = -f(0) = -3 \)
- For \( -x = -1 \) (which means \( x = 1 \)): \( -f(-(-1)) = -f(1) \). Compute \( f(1) = (1 + 2) + 1 = 4 \), so \( -f(1) = -4 \).
- For \( -x = -2 \) (which means \( x = 2 \)): \( -f(-(-2)) = -f(2) \). Compute \( f(2) = (2 + 2) + 1 = 5 \), so \( -f(2) = -5 \).

4. **Points for \( -f(-x) \)**:
- For \( x = 0 \): \( -f(-x) = -3 \)
- For \( x = 1 \): \( -f(-x) = -4 \)
- For \( x = 2 \): \( -f(-x) = -5 \)

So, the three points for \( -f(-x) \) are:

\[
\begin{array}{|c|c|}
\hline
x & -f(-x) \\
\hline
0 & -3 \\
1 & -4 \\
2 & -5 \\
\hline
\end{array}
\]