To determine which of the given tables represent a function, we need to use the definition of a function: A relationship between input values (x) and output values (y) in which each input value is associated with exactly one output value. This means that for each unique x-value, there must be only one corresponding y-value.
Let's analyze each table one by one:
### Table 1
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-3 & -1 \\
\hline
0 & 0 \\
\hline
-2 & -1 \\
\hline
8 & 1 \\
\hline
\end{array}
\][/tex]
- The pairs are (-3, -1), (0, 0), (-2, -1), and (8, 1).
- No x-value is repeated. Each x-value associates with one and only one y-value.
Since each x-value has a unique y-value, Table 1 does represent a function.
### Table 2
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-4 & 8 \\
\hline
-2 & 2 \\
\hline
-2 & 4 \\
\hline
0 & 2 \\
\hline
\end{array}
\][/tex]
- The pairs are (-4, 8), (-2, 2), (-2, 4), and (0, 2).
- Here, the x-value -2 is associated with two different y-values (2 and 4).
Since the x-value -2 is associated with two different y-values, Table 2 does not represent a function.
### Table 3
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-4 & 2 \\
\hline
3 & 5 \\
\hline
1 & 3 \\
\hline
-4 & 0 \\
\hline
\end{array}
\][/tex]
- The pairs are (-4, 2), (3, 5), (1, 3), and (-4, 0).
- Here, the x-value -4 is associated with two different y-values (2 and 0).
Since the x-value -4 is associated with two different y-values, Table 3 does not represent a function.
### Conclusion
Only Table 1 represents a function.
The result is:
- Table 1: Yes, it represents a function.
- Table 2: No, it does not represent a function.
- Table 3: No, it does not represent a function.
So, the table that represents a function is Table 1.
