Alright, let's walk through the given question step-by-step to understand and interpret the results.
### 1. The Set of Ordered Pairs
We have a given set of ordered pairs:
[tex]\[
\{ (-2, 4), (0, 2), (-1, 3), (4, -2) \}
\][/tex]
### 2. The Mapping Diagram for [tex]\( y = x^4 \)[/tex]
We need to map each [tex]\( x \)[/tex] from the ordered pairs to [tex]\( y \)[/tex] using the function [tex]\( y = x^4 \)[/tex].
Let's compute the function for each [tex]\( x \)[/tex]:
- For [tex]\( x = 4 \)[/tex]:
[tex]\[
y = 4^4 = 256
\][/tex]
- For [tex]\( x = 0 \)[/tex]:
[tex]\[
y = 0^4 = 0
\][/tex]
- For [tex]\( x = -1 \)[/tex]:
[tex]\[
y = (-1)^4 = 1
\][/tex]
- For [tex]\( x = -2 \)[/tex]:
[tex]\[
y = (-2)^4 = 16
\][/tex]
This gives the mapping diagram as:
[tex]\[
\{ 4 \rightarrow 256, 0 \rightarrow 0, -1 \rightarrow 1, -2 \rightarrow 16 \}
\][/tex]
### 3. The Given Table of Pairs
We also have a table of pairs:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $y$ \\
\hline
-3 & 5 \\
\hline
-1 & 2 \\
\hline
1 & -1 \\
\hline
-1 & 4 \\
\hline
\end{tabular}
\][/tex]
### Summary
To put it all together:
- The given set of ordered pairs is:
[tex]\[
\{(4, -2), (0, 2), (-1, 3), (-2, 4)\}
\][/tex]
- The mapping diagram based on [tex]\( y = x^4 \)[/tex] is:
[tex]\[
\{4 \rightarrow 256, 0 \rightarrow 0, -1 \rightarrow 1, -2 \rightarrow 16\}
\][/tex]
- The additional table of pairs provided is:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $y$ \\
\hline
-3 & 5 \\
\hline
-1 & 2 \\
\hline
1 & -1 \\
\hline
-1 & 4 \\
\hline
\end{tabular}
\][/tex]
Thus, we have consolidated and explained the information given comprehensively.
