Question

When f(x) = x3 is reflected vertically, the new function is f(x) =

Complete the table below for the vertical reflection of the function f(x) =x3

x −3 −2 −1 0 1 2 3
−f(x)

Answer 1

When a function \( f(x) \) is reflected vertically, the new function is given by \( -f(x) \).

Given \( f(x) = x^3 \), the new function after vertical reflection will be:

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

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

\[
\begin{array}{|c|c|c|}
\hline
x & f(x) = x^3 & -f(x) = -x^3 \\
\hline
-3 & (-3)^3 = -27 & -(-27) = 27 \\
-2 & (-2)^3 = -8 & -(-8) = 8 \\
-1 & (-1)^3 = -1 & -(-1) = 1 \\
0 & (0)^3 = 0 & -(0) = 0 \\
1 & (1)^3 = 1 & -(1) = -1 \\
2 & (2)^3 = 8 & -(8) = -8 \\
3 & (3)^3 = 27 & -(27) = -27 \\
\hline
\end{array}
\]

Thus, the completed table is:

\[
\begin{array}{|c|c|}
\hline
x & -f(x) \\
\hline
-3 & 27 \\
-2 & 8 \\
-1 & 1 \\
0 & 0 \\
1 & -1 \\
2 & -8 \\
3 & -27 \\
\hline
\end{array}
\]