Welcome to Westonci.ca, your one-stop destination for finding answers to all your questions. Join our expert community now! Our platform provides a seamless experience for finding precise answers from a network of experienced professionals. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
To determine which representation from the given data sets represents a function, we need to assess whether each set of points satisfies the definition of a function. Recall that a function is a relation where each input (or \( x \)-value) is associated with exactly one output (or \( y \)-value).
Let's examine each set of points separately:
1.
[tex]\[ \begin{tabular}{|c|c|} \hline [tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline
-5 & 10 \\
\hline
-3 & 5 \\
\hline
-3 & 4 \\
\hline
0 & 0 \\
\hline
5 & -10 \\
\hline
\end{tabular}
\][/tex]
Here, the \( x \)-value -3 is associated with two different \( y \)-values (5 and 4). This means that for \( x = -3 \), there are multiple outputs, which violates the definition of a function. Therefore, this set of points does not represent a function.
2.
[tex]\[ \{(-8, -2), (-4, 1), (0, -2), (2, 3), (4, -4)\} \][/tex]
In this set, each \( x \)-value corresponds to exactly one \( y \)-value. The \( x \)-values are: -8, -4, 0, 2, and 4, and all are unique with unique \( y \)-values associated with them. Hence, this set represents a function.
3.
[tex]\[ \begin{tabular}{|c|c|} \hline [tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline
-2 & -3 \\
\hline
-1 & -2 \\
\hline
0 & -1 \\
\hline
0 & 0 \\
\hline
1 & -1 \\
\hline
\end{tabular}
\][/tex]
Here, the \( x \)-value 0 has two different \( y \)-values (-1 and 0). This violates the definition of a function, as there cannot be two different \( y \)-values for the same \( x \)-value. Thus, this set does not represent a function.
4.
[tex]\[ \{(-12, 4), (-6, 10), (-4, 15), (-8, 18), (-12, 24)\} \][/tex]
In this set, the \( x \)-value -12 is associated with two different \( y \)-values (4 and 24). This means that for \( x = -12 \), there are multiple outputs, which violates the definition of a function. Therefore, this set does not represent a function.
After evaluating all four sets, we conclude that only the second set of points represents a function.
Let's examine each set of points separately:
1.
[tex]\[ \begin{tabular}{|c|c|} \hline [tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline
-5 & 10 \\
\hline
-3 & 5 \\
\hline
-3 & 4 \\
\hline
0 & 0 \\
\hline
5 & -10 \\
\hline
\end{tabular}
\][/tex]
Here, the \( x \)-value -3 is associated with two different \( y \)-values (5 and 4). This means that for \( x = -3 \), there are multiple outputs, which violates the definition of a function. Therefore, this set of points does not represent a function.
2.
[tex]\[ \{(-8, -2), (-4, 1), (0, -2), (2, 3), (4, -4)\} \][/tex]
In this set, each \( x \)-value corresponds to exactly one \( y \)-value. The \( x \)-values are: -8, -4, 0, 2, and 4, and all are unique with unique \( y \)-values associated with them. Hence, this set represents a function.
3.
[tex]\[ \begin{tabular}{|c|c|} \hline [tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline
-2 & -3 \\
\hline
-1 & -2 \\
\hline
0 & -1 \\
\hline
0 & 0 \\
\hline
1 & -1 \\
\hline
\end{tabular}
\][/tex]
Here, the \( x \)-value 0 has two different \( y \)-values (-1 and 0). This violates the definition of a function, as there cannot be two different \( y \)-values for the same \( x \)-value. Thus, this set does not represent a function.
4.
[tex]\[ \{(-12, 4), (-6, 10), (-4, 15), (-8, 18), (-12, 24)\} \][/tex]
In this set, the \( x \)-value -12 is associated with two different \( y \)-values (4 and 24). This means that for \( x = -12 \), there are multiple outputs, which violates the definition of a function. Therefore, this set does not represent a function.
After evaluating all four sets, we conclude that only the second set of points represents a function.
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.