To determine if a table of values represents a function, we need to check whether each input, or [tex]\( x \)[/tex] value, corresponds to exactly one output, or [tex]\( y \)[/tex] value. A function is a relation where each [tex]\( x \)[/tex] value has a unique [tex]\( y \)[/tex] value.
The given table is:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-5 & 10 \\
\hline
-3 & 5 \\
\hline
-3 & 4 \\
\hline
0 & 0 \\
\hline
5 & -10 \\
\hline
\end{array}
\][/tex]
Here are the steps to determine if this table represents a function:
1. List all the [tex]\( x \)[/tex] values:
- [tex]\( x = -5 \)[/tex]
- [tex]\( x = -3 \)[/tex]
- [tex]\( x = -3 \)[/tex]
- [tex]\( x = 0 \)[/tex]
- [tex]\( x = 5 \)[/tex]
2. Check for repeated [tex]\( x \)[/tex] values:
- [tex]\( x = -3 \)[/tex] appears twice with different [tex]\( y \)[/tex] values (5 and 4).
In a function, each [tex]\( x \)[/tex] value must map to exactly one [tex]\( y \)[/tex] value. Since [tex]\( x = -3 \)[/tex] maps to both 5 and 4, this violates the definition of a function. Therefore, the table does not represent a function.
Thus, the answer is:
This table does not represent a function.
