Does this table represent a function? Why or why not?
\begin{tabular}{|c|c|}
\hline$x$ & $y$ \\
\hline 4 & 0 \\
\hline 7 & 5 \\
\hline 8 & 5 \\
\hline 8 & 8 \\
\hline 10 & 9 \\
\hline
\end{tabular}
A. Yes, because every $x$-value corresponds to exactly one $y$-value.
B. Yes, because there are two $x$-values that are the same.
C. No, because one $x$-value corresponds to two different $y$-values.
D. No, because two of the $y$-values are the same.
Answer (1)
A table represents a function if each x -value corresponds to exactly one y -value.
In the given table, the x -value 8 corresponds to two different y -values: 5 and 8.
Therefore, the table does not represent a function.
The correct answer is C: No, because one x -value corresponds to two different y -values.
Explanation
Checking the Definition of a Function To determine if the table represents a function, we need to check if each x -value corresponds to exactly one y -value. In other words, no x -value can be paired with two different y -values.
Identifying the Issue Looking at the table, we see that when x = 8 , the table shows two different y -values: y = 5 and y = 8 . This means that the x -value 8 is associated with two different y -values.
Conclusion Since the x -value 8 corresponds to two different y -values (5 and 8), the table does not represent a function. Therefore, the correct answer is C.
Examples
Imagine you are assigning tasks to workers. If one worker (x-value) is assigned to two different tasks (y-values) at the same time, it creates confusion and the assignment is not a function. Similarly, in mathematics, for a relation to be a function, each input (x-value) must have only one output (y-value). This concept is crucial in various fields like computer science, engineering, and economics, where clear and unique relationships are necessary for accurate modeling and prediction.
