Question

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
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 find the points of the function \( h(x) \) which is the reflection of \( f(x) \) about the origin, we apply the transformation:

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

This means we will switch the signs of both \( x \) and \( f(x) \). Using the values given in the table for \( f(x) \):

\[
\begin{align*}
f(-4) &= 8 \quad \Rightarrow \quad h(4) = -f(-4) = -8 \\
f(-3) &= 2 \quad \Rightarrow \quad h(3) = -f(-3) = -2 \\
f(-2) &= 0 \quad \Rightarrow \quad h(2) = -f(-2) = 0 \\
f(-1) &= 2 \quad \Rightarrow \quad h(1) = -f(-1) = -2 \\
f(0) &= 8 \quad \Rightarrow \quad h(0) = -f(0) = -8 \\
\end{align*}
\]

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

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

So the completed table is:

\[
\begin{align*}
x & h(x) \\
4 & -8 \\
3 & -2 \\
2 & 0 \\
1 & -2 \\
0 & -8 \\
\end{align*}
\]

Answer 2

Table again please mine was blurry

Answer 3

Certainly! Here is the completed table for \( h(x) \):

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

If you have any further questions, feel free to ask!

Answer 4

I’m sorry but it says completed table but then it’s not there

Answer 5

I apologize for the misunderstanding. Here’s the completed table clearly presented:

| **x** | **h(x)** |
|-------|----------|
| 4 | -8 |
| 3 | -2 |
| 2 | 0 |
| 1 | -2 |
| 0 | -8 |

Thank you for your patience, and let me know if there’s anything else you need!