To determine if the given table represents a function, we need to recall the definition of a function. A function is defined as a relation where every input \( x \) corresponds to exactly one output \( y \). In other words, each \( x \) value must map to one and only one \( y \) value.
Let's analyze the table:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
2 & 1 \\
\hline
2 & 4 \\
\hline
3 & 4 \\
\hline
4 & 2 \\
\hline
5 & 5 \\
\hline
\end{array}
\][/tex]
1. For \( x = 2 \), we have two outputs: \( y = 1 \) and \( y = 4 \). This means that the input \( x = 2 \) corresponds to two different \( y \) values, which violates the definition of a function.
2. Other \( x \) values (3, 4, and 5) each map to a single \( y \) value.
Given this analysis, the table does not represent a function because the input \( x = 2 \) yields two different outputs. Therefore, the correct reasoning is:
D. No, because one [tex]\( x \)[/tex]-value corresponds to two different [tex]\( y \)[/tex]-values.
