Questions: Use the following input-output table given in the first column. Is the relation a function? If so, match them with their domain and range.
Input Output
------ ------
3 0
6 4
9 0
12 -4
Input Output
------ ------
2 2
8 6
2 1
10 -6
Input Output
------ ------
1 2
3 4
5 4
7 6
NOT a function
Domain: 1,3,5,7
Range : 2,4,6
Domain : 3,6,9,12
Range : -4,0,4
Transcript text: Use the following input-output table given in the first column. Is the relation a function? If so, match them with their domain and range.
\begin{tabular}{|c|c|}
\hline \multicolumn{2}{|c|}{ Input } \\
\hline 3 & 0 \\
\hline 6 & 4 \\
\hline 9 & 0 \\
\hline 12 & -4 \\
\hline
\end{tabular}
\begin{tabular}{|c|c|}
\hline Input & Output \\
\hline 2 & 2 \\
\hline 8 & 6 \\
\hline 2 & 1 \\
\hline 10 & -6 \\
\hline
\end{tabular}
\begin{tabular}{|c|c|}
\hline Input & Output \\
\hline 1 & 2 \\
\hline 3 & 4 \\
\hline 5 & 4 \\
\hline 7 & 6 \\
\hline
\end{tabular}
NOT a function
Domain: $\{1,3,5,7\}$
Range : $\{2,4,6\}$
Domain : $\{3,6,9,12\}$
Range : $\{-4,0,4\}$
Solution
Solution Steps
Step 1: Analyze the first table
The first table represents a function because each input has only one output. The domain is {3, 6, 9, 12} and the range is {-4, 0, 4}.
Step 2: Analyze the second table
The second table does _not_ represent a function because the input '2' has two different outputs: 2 and 1.
Step 3: Analyze the third table
The third table represents a function because each input has only one output. The domain is {1, 3, 5, 7} and the range is {2, 4, 6}.
Final Answer
The first table matches with "Domain: {3, 6, 9, 12} Range: {-4, 0, 4}". The second table matches with "NOT a function". The third table matches with "Domain: {1, 3, 5, 7} Range: {2, 4, 6}".