Question

When f(x) = x^3 is reflected horizontally the new function is f(x) = __
Complete the table
x -3 -2 -1 0 1 2 3
-f(x) __ __ __ __ __ _ __

Answer 1

When the function \( f(x) = x^3 \) is reflected horizontally, the new function becomes \( f(x) = -x^3 \) (since reflecting horizontally involves negating the input to the function, resulting in negating the output).

To complete the table, we need to calculate \( -f(x) \) for each value of \( x \):

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

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

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

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

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

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

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

Now, we can fill in the table as follows:

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

So, the completed table is:

\[
x -3 -2 -1 0 1 2 3 \\
-f(x) 27 8 1 0 -1 -8 -27
\]