Question

If the function is f(x)=x^3 complete the table for its horizontal reflection
x 0 1 2
f(-x)

Answer 1

To find the values of the function \( f(-x) \) when the original function is given as \( f(x) = x^3 \), we first need to compute \( f(-x) \).

The function can be rewritten as:
\[
f(-x) = (-x)^3
\]
Since \((-x)^3 = -x^3\), the function \( f(-x) \) can be expressed as:
\[
f(-x) = -x^3
\]

Now, we can compute the values of \( f(-x) \) for the given \( x \) values in the table.

- 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 complete 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:

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