The table’s purpose is to determine whether it represents a function. To establish this, let us recall the definition of a function in mathematical terms:
A relation is a function if and only if each input value (commonly referred to as [tex]\( x \)[/tex]) maps to exactly one output value (commonly referred to as [tex]\( y \)[/tex]). This means no [tex]\( x \)[/tex]-value is associated with more than one [tex]\( y \)[/tex]-value.
Let's examine the given table:
\begin{tabular}{|c|c|}
\hline
\textbf{Hours of Training} & \textbf{Monthly Pay} \\
\hline
10 & 1250 \\
\hline
20 & 1400 \\
\hline
30 & 1550 \\
\hline
40 & 1700 \\
\hline
50 & 1850 \\
\hline
60 & 2000 \\
\hline
70 & 2150 \\
\hline
\end{tabular}
1. Identify the [tex]\( x \)[/tex]-values (inputs):
- The [tex]\( x \)[/tex]-values are: 10, 20, 30, 40, 50, 60, 70.
2. Check for uniqueness among [tex]\( x \)[/tex]-values:
- Each [tex]\( x \)[/tex]-value is unique. None of the [tex]\( x \)[/tex]-values is repeated.
Due to the uniqueness of [tex]\( x \)[/tex]-values and the fact that each [tex]\( x \)[/tex]-value maps to a single [tex]\( y \)[/tex]-value, this relationship satisfies the condition of being a function.
Thus, the correct answer is:
Since each [tex]\( x \)[/tex]-value (Hours of Training) is different and maps to exactly one [tex]\( y \)[/tex]-value (Monthly Pay), this table represents a function.
C. Yes, because each [tex]\( x \)[/tex]-value is different and maps to exactly one [tex]\( y \)[/tex]-value.
