Question

4.

The table shows the points of a function. Complete the table to show the points after a reflection about the origin.

x f(x)
-4 8
-3 2
-2 0
-1 2
0 8

(5 points)
Complete the table to show that h(x)
is the reflection about the origin of the function f(x)


x h(x)
4
3
2
1
0

Answer 1

To reflect a point \((x, f(x))\) about the origin, we transform it to the point \((-x, -f(x))\).

Starting with the given points:

\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-4 & 8 \\
-3 & 2 \\
-2 & 0 \\
-1 & 2 \\
0 & 8 \\
\hline
\end{array}
\]

We need to find \( h(x) \) for corresponding positive \( x \) values:

1. For \( x = 4 \) (which reflects to \( -4 \)):
\( h(4) = -f(-4) = -8 \)

2. For \( x = 3 \) (which reflects to \( -3 \)):
\( h(3) = -f(-3) = -2 \)

3. For \( x = 2 \) (which reflects to \( -2 \)):
\( h(2) = -f(-2) = -0 = 0 \)

4. For \( x = 1 \) (which reflects to \( -1 \)):
\( h(1) = -f(-1) = -2 \)

5. For \( x = 0 \):
Since reflecting at zero keeps it the same, \( h(0) = -f(0) = -8 \)

Now we can populate the table:

\[
\begin{array}{|c|c|}
\hline
x & h(x) \\
\hline
4 & -8 \\
3 & -2 \\
2 & 0 \\
1 & -2 \\
0 & -8 \\
\hline
\end{array}
\]

Thus, the completed table showing the reflection about the origin is:

\[
\begin{array}{|c|c|}
\hline
x & h(x) \\
\hline
4 & -8 \\
3 & -2 \\
2 & 0 \\
1 & -2 \\
0 & -8 \\
\hline
\end{array}
\]