Question

If the function is f (x) = x^3 complete the table for its horizontal reflection.

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

Answer 1

To find the values of \( f(-x) \) for the function \( f(x) = x^3 \), we can substitute \(-x\) into the function.

The function becomes:
\[
f(-x) = (-x)^3 = -x^3
\]

Now we can complete the table:

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

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

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

Now, populating the table:

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

So the completed table is:

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