tripyy18
Answered

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Given the following information, complete the associated tasks.

1. The set of ordered pairs:
[tex]\[
\{(-2,4), (0,2), (-1,3), (4,-2)\}
\][/tex]

2. The mapping diagram:
[tex]\[
\square
\][/tex]

3. The function:
[tex]\[
y = x^4
\][/tex]
[tex]\[
\square
\][/tex]

4. The table:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $y$ \\
\hline
-3 & 5 \\
\hline
-1 & 2 \\
\hline
1 & -1 \\
\hline
-1 & 4 \\
\hline
\end{tabular}
\][/tex]
[tex]\[
\square
\][/tex]

Sagot :

GinnyAnswer
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.
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