Question

the function is f(x)=x^3
, complete the table for its horizontal reflection.(2 points)
x 0 1 2
f(−x)

Answer 1

To find the horizontal reflection of the function \( f(x) = x^3 \), we need to evaluate \( f(-x) \) for the values of \( x \) in the table.

1. **Calculate \( f(-x) \)** for given \( x \):
- For \( x = 0 \):
\[
f(-0) = (-0)^3 = 0
\]
- For \( x = 1 \):
\[
f(-1) = (-1)^3 = -1
\]
- For \( x = 2 \):
\[
f(-2) = (-2)^3 = -8
\]

2. **Complete the table**:

\[
\begin{array}{|c|c|c|}
\hline
x & f(-x) \\
\hline
0 & 0 \\
1 & -1 \\
2 & -8 \\
\hline
\end{array}
\]

So, the completed table for \( f(-x) \) is:

- For \( x = 0 \), \( f(-0) = 0 \)
- For \( x = 1 \), \( f(-1) = -1 \)
- For \( x = 2 \), \( f(-2) = -8 \)

The values are:
- \( f(-0) = 0 \)
- \( f(-1) = -1 \)
- \( f(-2) = -8 \)