To determine if a set of points represents a function, we need to check if each input (x-value) has exactly one output (y-value). In other words, no x-value should repeat in a way that it corresponds to different y-values.
Let's investigate each set provided:
1. Table:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-10 & 84 \\
\hline
-5 & 31.5 \\
\hline
0 & 4 \\
\hline
5 & 1.5 \\
\hline
10 & 24 \\
\hline
\end{array}
\][/tex]
For the table, each x-value (-10, -5, 0, 5, 10) is unique, meaning that each x-value is paired with exactly one y-value. Therefore, this set of points represents a function.
2. Set of Points: [tex]\((4,5), (6,-2), (-5,0), (6,1)\)[/tex]
For this set, let's look at the x-values: 4, 6, -5, 6. Here, the x-value 6 is repeated, but it corresponds to two different y-values (-2 and 1). This violates the definition of a function, where each x-value should pair with exactly one y-value.
Therefore, this set of points does not represent a function.
### Conclusion
- The table of points with x-values -10, -5, 0, 5, and 10 represents a function.
- The set of points [tex]\((4,5), (6,-2), (-5,0), (6,1)\)[/tex] does not represent a function.
