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Question 20 of 25

What is the domain of the function shown in the table?

\begin{tabular}{|c|c|}
\hline
[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline
2 & 3 \\
\hline
4 & 4 \\
\hline
6 & 5 \\
\hline
8 & 6 \\
\hline
\end{tabular}

A. [tex]$\{2,3,4,5,6,8\}$[/tex]

B. [tex]$(2,3),(4,4),(6,5),(8,6)$[/tex]

C. [tex]$\{2,4,6,8\}$[/tex]

D. [tex]$\{3,4,5,6\}$[/tex]



Answer :

GinnyAnswer
To determine the domain of a function, we need to identify all the possible input values (x-values) for which the function is defined. The table given shows pairs of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] values:

[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline 2 & 3 \\ \hline 4 & 4 \\ \hline 6 & 5 \\ \hline 8 & 6 \\ \hline \end{array} \][/tex]

We extract the [tex]\( x \)[/tex]-values from the table:
- [tex]\( x = 2 \)[/tex]
- [tex]\( x = 4 \)[/tex]
- [tex]\( x = 6 \)[/tex]
- [tex]\( x = 8 \)[/tex]

Collectively, the set of all [tex]\( x \)[/tex]-values given in the table is [tex]\(\{2, 4, 6, 8\}\)[/tex]. So, we conclude that the domain of the function is the set of these [tex]\( x \)[/tex]-values.

Therefore, the correct answer is:

C. [tex]\(\{2, 4, 6, 8\}\)[/tex]