Answered

Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Connect with professionals ready to provide precise answers to your questions on our comprehensive Q&A platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

Which table represents a function?

Table 1:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $y$ \\
\hline
-3 & -1 \\
\hline
0 & 0 \\
\hline
-2 & -1 \\
\hline
8 & 1 \\
\hline
\end{tabular}
\][/tex]

Table 2:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $y$ \\
\hline
-5 & -5 \\
\hline
0 & 0 \\
\hline
-5 & 5 \\
\hline
6 & -6 \\
\hline
\end{tabular}
\][/tex]

Table 3:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $y$ \\
\hline
-4 & 8 \\
\hline
-2 & 2 \\
\hline
-2 & 4 \\
\hline
0 & 2 \\
\hline
\end{tabular}
\][/tex]

Table 4:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $y$ \\
\hline
-4 & 2 \\
\hline
3 & 5 \\
\hline
1 & 3 \\
\hline
-4 & 0 \\
\hline
\end{tabular}
\][/tex]

Sagot :

GinnyAnswer
Certainly! Let's determine which of these tables represents a function. Recall that a relation (table of [tex]\((x, y)\)[/tex] pairs) is a function if every [tex]\(x\)[/tex] value corresponds to exactly one [tex]\(y\)[/tex] value. In other words, for each [tex]\(x\)[/tex] value, there should be only one [tex]\(y\)[/tex] value associated with it.

Let’s analyze each table one by one.

### Table 1
[tex]\[ \begin{tabular}{|c|c|} \hline$x$ & $y$ \\ \hline-3 & -1 \\ \hline 0 & 0 \\ \hline-2 & -1 \\ \hline 8 & 1 \\ \hline \end{tabular} \][/tex]
- x = -3 corresponds to y = -1
- x = 0 corresponds to y = 0
- x = -2 corresponds to y = -1
- x = 8 corresponds to y = 1

All [tex]\(x\)[/tex] values are unique. Therefore, Table 1 represents a function.

### Table 2
[tex]\[ \begin{tabular}{|c|c|} \hline$x$ & $y$ \\ \hline-5 & -5 \\ \hline 0 & 0 \\ \hline-5 & 5 \\ \hline 6 & -6 \\ \hline \end{tabular} \][/tex]
- x = -5 corresponds to y = -5
- x = 0 corresponds to y = 0
- x = -5 corresponds to y = 5
- x = 6 corresponds to y = -6

The [tex]\(x\)[/tex] value -5 corresponds to both y = -5 and y = 5. Therefore, Table 2 does not represent a function.

### Table 3
[tex]\[ \begin{tabular}{|c|c|} \hline$x$ & $y$ \\ \hline-4 & 8 \\ \hline-2 & 2 \\ \hline-2 & 4 \\ \hline 0 & 2 \\ \hline \end{tabular} \][/tex]
- x = -4 corresponds to y = 8
- x = -2 corresponds to y = 2
- x = -2 corresponds to y = 4
- x = 0 corresponds to y = 2

The [tex]\(x\)[/tex] value -2 corresponds to both y = 2 and y = 4. Therefore, Table 3 does not represent a function.

### Table 4
[tex]\[ \begin{tabular}{|c|c|} \hline$x$ & $y$ \\ \hline-4 & 2 \\ \hline 3 & 5 \\ \hline 1 & 3 \\ \hline-4 & 0 \\ \hline \end{tabular} \][/tex]
- x = -4 corresponds to y = 2
- x = 3 corresponds to y = 5
- x = 1 corresponds to y = 3
- x = -4 corresponds to y = 0

The [tex]\(x\)[/tex] value -4 corresponds to both y = 2 and y = 0. Therefore, Table 4 does not represent a function.

### Conclusion
Only Table 1 represents a function, as it is the only table where each [tex]\(x\)[/tex] value is associated with exactly one [tex]\(y\)[/tex] value.
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.