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Determining if a Table of Values Represents a Function

Which represents a function?

1.
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $y$ \\
\hline
-5 & 10 \\
\hline
-3 & 5 \\
\hline
-3 & 4 \\
\hline
0 & 0 \\
\hline
5 & -10 \\
\hline
\end{tabular}
\][/tex]

2.
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $y$ \\
\hline
-8 & -2 \\
\hline
-4 & 1 \\
\hline
0 & -2 \\
\hline
2 & 3 \\
\hline
4 & -4 \\
\hline
\end{tabular}
\][/tex]

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

4.
[tex]\[
\begin{array}{c}
\{(-12,4),(-6,10), \\
(-4,15),(-8,18), \\
(-12,24)\}
\end{array}
\][/tex]



Answer :

GinnyAnswer
To determine if a table of values represents a function, we need to check whether each input, or [tex]\( x \)[/tex] value, corresponds to exactly one output, or [tex]\( y \)[/tex] value. A function is a relation where each [tex]\( x \)[/tex] value has a unique [tex]\( y \)[/tex] value.

The given table is:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline -5 & 10 \\ \hline -3 & 5 \\ \hline -3 & 4 \\ \hline 0 & 0 \\ \hline 5 & -10 \\ \hline \end{array} \][/tex]

Here are the steps to determine if this table represents a function:

1. List all the [tex]\( x \)[/tex] values:
- [tex]\( x = -5 \)[/tex]
- [tex]\( x = -3 \)[/tex]
- [tex]\( x = -3 \)[/tex]
- [tex]\( x = 0 \)[/tex]
- [tex]\( x = 5 \)[/tex]

2. Check for repeated [tex]\( x \)[/tex] values:
- [tex]\( x = -3 \)[/tex] appears twice with different [tex]\( y \)[/tex] values (5 and 4).

In a function, each [tex]\( x \)[/tex] value must map to exactly one [tex]\( y \)[/tex] value. Since [tex]\( x = -3 \)[/tex] maps to both 5 and 4, this violates the definition of a function. Therefore, the table does not represent a function.

Thus, the answer is:

This table does not represent a function.

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