Question

If the function is f(x)=x3
𝑓
(
𝑥
)
=
𝑥
3
, complete the table for its horizontal reflection.(2 points)
x 0 1 2
f(−x)
𝑓
(
−
𝑥
)

Answer 1

To find the horizontal reflection of the function \( f(x) = x^3 \), we evaluate \( f(-x) \).

1. Substitute \(-x\) into the function:
\[
f(-x) = (-x)^3
\]

2. Simplifying the expression:
\[
(-x)^3 = -x^3
\]

So, we want to compute \( f(-x) \) for the given values of \( x \) in the table.

### Table for \( f(-x) \):
- When \( x = 0 \):
\[
f(-0) = -0^3 = 0
\]

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

- When \( x = 2 \):
\[
f(-2) = -2^3 = -8
\]

Now, we can fill in the table:

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

Therefore, the completed table looks like this:

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