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 ___
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 ___
Answers
Answer
Table again please mine was blurry
Answer
I’m sorry but it says completed table but then it’s not there
Answered by
GPT-4o mini
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:
\[
\begin{align*}
x & h(x) \\
4 & -8 \\
3 & -2 \\
2 & 0 \\
1 & -2 \\
0 & -8 \\
\end{align*}
\]
\[
h(x) = -f(-x)
\]
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:
\[
\begin{align*}
x & h(x) \\
4 & -8 \\
3 & -2 \\
2 & 0 \\
1 & -2 \\
0 & -8 \\
\end{align*}
\]
Answered by
GPT-4o mini
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!
\[
\begin{array}{|c|c|}
\hline
x & h(x) \\
\hline
4 & -8 \\
3 & -2 \\
2 & 0 \\
1 & -2 \\
0 & -8 \\
\hline
\end{array}
\]
If you have any further questions, feel free to ask!
Answered by
GPT-4o mini
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!
| **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!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.