Let's work through the problem step-by-step:
1. Given Set of Ordered Pairs:
[tex]\[ \{(-2, 4), (0, 2), (-1, 3), (4, -2)\} \][/tex]
This is a set of pairs where each pair [tex]\((x, y)\)[/tex] is given.
2. Calculate [tex]\( y = x^4 \)[/tex] for Each Given Value of [tex]\( x \)[/tex]:
For each [tex]\(x\)[/tex] in the given ordered pairs, we need to compute [tex]\( y = x^4 \)[/tex]:
- For [tex]\((-2, 4)\)[/tex], [tex]\( x = -2 \)[/tex]:
[tex]\[ y = (-2)^4 = 16 \][/tex]
- For [tex]\((0, 2)\)[/tex], [tex]\( x = 0 \)[/tex]:
[tex]\[ y = 0^4 = 0 \][/tex]
- For [tex]\((-1, 3)\)[/tex], [tex]\( x = -1 \)[/tex]:
[tex]\[ y = (-1)^4 = 1 \][/tex]
- For [tex]\((4, -2)\)[/tex], [tex]\( x = 4 \)[/tex]:
[tex]\[ y = 4^4 = 256 \][/tex]
Thus, we have the [tex]\( y \)[/tex] values calculated for the corresponding [tex]\( x \)[/tex]-values as:
[tex]\[ \{256, 0, 1, 16\} \][/tex]
3. Given Table:
The given table 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]
4. Calculate [tex]\( y = x^4 \)[/tex] for Each [tex]\( x \)[/tex] in the Table:
- For [tex]\( x = -3 \)[/tex]:
[tex]\[ y = (-3)^4 = 81 \][/tex]
- For [tex]\( x = -1 \)[/tex]:
[tex]\[ y = (-1)^4 = 1 \][/tex]
- For [tex]\( x = 1 \)[/tex]:
[tex]\[ y = 1^4 = 1 \][/tex]
- For the other [tex]\( x = -1 \)[/tex]:
[tex]\[ y = (-1)^4 = 1 \][/tex]
Thus, the computed [tex]\( y \)[/tex]-values for the table are:
[tex]\[ \{81, 1, 1, 1\} \][/tex]
Summarized Answer:
- The given set of ordered pairs: [tex]\[\{(-2, 4), (0, 2), (-1, 3), (4, -2)\}\][/tex]
- The computed [tex]\( y \)[/tex] values for [tex]\( y = x^4 \)[/tex] from the ordered pairs: [tex]\[ \{256, 0, 1, 16\} \][/tex]
- The given table of [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $y$ \\
\hline
-3 & 5 \\
\hline
-1 & 2 \\
\hline
1 & -1 \\
\hline
-1 & 4 \\
\hline
\end{tabular}
\][/tex]
- The computed [tex]\( y \)[/tex] values for [tex]\( y = x^4 \)[/tex] from the table [tex]\( x \)[/tex]-values: [tex]\[ \{81, 1, 1, 1\} \][/tex]
These results comprehensively answer the question by detailing each step involved in calculating the specified values.
