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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 :

GinnyAnsweridn
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.
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