To determine the domain of the function based on the input-output table provided, we need to identify the set of all possible input values - in this context, the "Hours of training". These represent the values for which the function is defined.
Here is the table provided:
\begin{tabular}{|c|c|}
\hline Hours of training & Pay per month \\
\hline 5 & 100 \\
\hline 10 & 105 \\
\hline 15 & 110 \\
\hline 20 & 115 \\
\hline 25 & 120 \\
\hline 30 & 125 \\
\hline 35 & 130 \\
\hline
\end{tabular}
The hours of training (inputs) listed in the table are:
- 5
- 10
- 15
- 20
- 25
- 30
- 35
The domain of the function includes all these input values. Therefore, the domain is the set of hours of training.
Option A, [tex]$\{5, 100, 10, 105, 15, 110, 20\}$[/tex], includes both hours of training and pay per month values, which is not correct because it mixes inputs and outputs.
Option B, [tex]$\{100, 105, 110, 115, 120, 125, 130\}$[/tex], represents the pay per month (outputs) and not the domain.
Option C, [tex]$\{5, 10, 15, 20, 25, 30, 35\}$[/tex], correctly lists all the hours of training values (the inputs), and thus represents the domain of the function.
Option D, [tex]$\{130, 35, 125, 30, 120, 25, 115\}$[/tex], includes both pay per month values and hours of training values, but it is a mixed and incorrect representation of the domain.
Thus, the correct answer is:
C. [tex]$\{5, 10, 15, 20, 25, 30, 35\}$[/tex]
