Question

Complete the table to show that h(x)
is the reflection about the origin of the function f(x)
.(2 points)
x f(x)
0 0
1 1
2 8
x h(x)
0 0
Remaining Attempts : 3
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page 7 of 8

Answer 1

To show that \( h(x) \) is the reflection about the origin of the function \( f(x) \), we need to understand what that means in terms of function values.

If \( f(x) \) reflects about the origin, then \( h(x) \) will be defined as:

\[
h(x) = -f(x)
\]

This means that for each \( x \), the value of \( h(x) \) is the negative of the corresponding \( f(x) \) value.

Let’s complete the table based on the given values of \( f(x) \).

Given:
- \( f(0) = 0 \)
- \( f(1) = 1 \)
- \( f(2) = 8 \)

We can now calculate \( h(x) \):

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

Thus, the completed table is:

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

This shows that \( h(x) \) is indeed the reflection of \( f(x) \) about the origin.