Answered

Explore Westonci.ca, the top Q&A platform where your questions are answered by professionals and enthusiasts alike. Our platform provides a seamless experience for finding precise answers from a network of experienced professionals. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

Which table represents a function?

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

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

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

[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
To determine which table represents a function, we need to check if every [tex]\( x \)[/tex] value (input) maps to exactly one [tex]\( y \)[/tex] value (output). Let's consider each table.

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

In Table 1, we see that each [tex]\( x \)[/tex] value corresponds to one unique [tex]\( y \)[/tex] value:
- [tex]\( x = -3 \)[/tex] maps to [tex]\( y = -1 \)[/tex]
- [tex]\( x = 0 \)[/tex] maps to [tex]\( y = 0 \)[/tex]
- [tex]\( x = -2 \)[/tex] maps to [tex]\( y = -1 \)[/tex]
- [tex]\( x = 8 \)[/tex] maps to [tex]\( y = 1 \)[/tex]

Since no [tex]\( x \)[/tex] value is repeated with a different [tex]\( y \)[/tex] value, this table represents a function.

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

In Table 2, the [tex]\( x = -5 \)[/tex] corresponds to two different [tex]\( y \)[/tex] values:
- [tex]\( x = -5 \)[/tex] maps to [tex]\( y = -5 \)[/tex]
- [tex]\( x = -5 \)[/tex] maps to [tex]\( y = 5 \)[/tex]

Because an [tex]\( x \)[/tex] value is repeated with a different [tex]\( y \)[/tex] value, this table does not represent a function.

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

In Table 3, the [tex]\( x = -2 \)[/tex] corresponds to two different [tex]\( y \)[/tex] values:
- [tex]\( x = -2 \)[/tex] maps to [tex]\( y = 2 \)[/tex]
- [tex]\( x = -2 \)[/tex] maps to [tex]\( y = 4 \)[/tex]

Because an [tex]\( x \)[/tex] value is repeated with a different [tex]\( y \)[/tex] value, this table does not represent a function.

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

In Table 4, the [tex]\( x = -4 \)[/tex] corresponds to two different [tex]\( y \)[/tex] values:
- [tex]\( x = -4 \)[/tex] maps to [tex]\( y = 2 \)[/tex]
- [tex]\( x = -4 \)[/tex] maps to [tex]\( y = 0 \)[/tex]

Because an [tex]\( x \)[/tex] value is repeated with a different [tex]\( y \)[/tex] value, this table does not represent a function.

### Conclusion
Among the tables presented:
- Table 1 represents a function.
- Table 2, Table 3, and Table 4 do not represent functions.
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.