Question

If the function is f(x)=x3
, 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 \( f(-x) \).

Given that \( f(x) = x^3 \), we have:

\[
f(-x) = (-x)^3 = -x^3
\]

Now we can compute \( f(-x) \) for the given values of \( x \):

1. For \( x = 0 \):
\[
f(0) = -0^3 = 0
\]

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

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

Now we can complete the table for \( f(-x) \):

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

So, the completed table is:

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