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

To find the function that reflects \( f(x) = x^3 \) vertically, we need to take the negative of the function. Thus, the new function will be:

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

Now, let’s complete the table by calculating \( -f(x) \) for the given values of \( x \):

1. For \( x = -3 \):
\[
f(-3) = -(-3^3) = -(-27) = 27
\]

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

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

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

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

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

7. For \( x = 3 \):
\[
f(3) = -(3^3) = -27
\]

Now, we can fill in the table:

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

So, the completed table is shown above.