To determine which of the given options represents a function, we need to review each option and check if every input maps to exactly one output.
### Option C
The table of values is given as:
\begin{tabular}{|c|c|c|c|c|c|}
\hline[tex]$x$[/tex] & -5 & -1 & 9 & 8 & -1 \\
\hline[tex]$y$[/tex] & 1 & 7 & 23 & 17 & 1 \\
\hline
\end{tabular}
- For [tex]\(x = -5\)[/tex], [tex]\(y = 1\)[/tex]
- For [tex]\(x = -1\)[/tex], [tex]\(y = 7\)[/tex]
- For [tex]\(x = 9\)[/tex], [tex]\(y = 23\)[/tex]
- For [tex]\(x = 8\)[/tex], [tex]\(y = 17\)[/tex]
- For [tex]\(x = -1\)[/tex], [tex]\(y = 1\)[/tex]
Here, [tex]\(x = -1\)[/tex] maps to both [tex]\(y = 7\)[/tex] and [tex]\(y = 1\)[/tex]. Therefore, one input [tex]\(x = -1\)[/tex] has multiple outputs. This violates the definition of a function.
### Option D
The set of points is given as: [tex]\(\{(0,1),(3,2),(-8,3),(-7,2),(3,4)\}\)[/tex]
- For [tex]\(x = 0\)[/tex], [tex]\(y = 1\)[/tex]
- For [tex]\(x = 3\)[/tex], [tex]\(y = 2\)[/tex]
- For [tex]\(x = -8\)[/tex], [tex]\(y = 3\)[/tex]
- For [tex]\(x = -7\)[/tex], [tex]\(y = 2\)[/tex]
- For [tex]\(x = 3\)[/tex], [tex]\(y = 4\)[/tex]
Here, [tex]\(x = 3\)[/tex] maps to both [tex]\(y = 2\)[/tex] and [tex]\(y = 4\)[/tex]. Again, one input [tex]\(x = 3\)[/tex] has multiple outputs. This violates the definition of a function.
### Conclusion
Both Option C and Option D do not satisfy the definition of a function because they each contain an input that maps to multiple outputs.
Options A and B are not clearly described and cannot be evaluated without more information.
Thus, based on the given information, it is not possible to definitively determine which of the provided options represents a function.
