Question

Complete the table to show that h(x)
is the reflection about the x-axis of the function f(x)

x f(x)
0 0
1 1
2 8
x h(x)
0 0

Answer 1

To show that \( h(x) \) is the reflection about the x-axis of the function \( f(x) \), we need to reflect each value of \( f(x) \) into \( h(x) \).

The reflection about the x-axis can be accomplished by negating the output values of \( f(x) \). Therefore, if \( f(x) \) provides values \( f(x) \), then \( h(x) = -f(x) \).

Let's complete the table:

1. For \( x = 0 \):
- \( f(0) = 0 \)
- \( h(0) = -f(0) = -0 = 0 \)

2. For \( x = 1 \):
- \( f(1) = 1 \)
- \( h(1) = -f(1) = -1 \)

3. For \( x = 2 \):
- \( f(2) = 8 \)
- \( h(2) = -f(2) = -8 \)

Now, we can fill in the table for \( h(x) \):

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

So, the completed table is:

| x | h(x) |
|-----|----------|
| 0 | 0 |
| 1 | -1 |
| 2 | -8 |