Question

Part B: Complete the table below for the horizontal reflection of the function f(x) =x3
fill in the table
x
−3
−2
−1
0 1 2 3
−f(x)

Answer 1

To find the horizontal reflection of the function \( f(x) = x^3 \), we need to compute \( -f(x) \). This means we will take the function values at the given \( x \) values and multiply them by -1.

First, we'll compute \( f(x) = x^3 \) for each \( x \) value and then take the negative of that value to get \( -f(x) \).

Here are the calculations:

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

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

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

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

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:

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