Answer :
To determine if the given table represents a function, we need to review the definition of a function. A function is a relationship between inputs and outputs where each input is associated with exactly one output.
Given 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]
Let's examine each pair of values:
1. For [tex]\( x = 2 \)[/tex], we have two corresponding [tex]\( y \)[/tex]-values: [tex]\( y = 1 \)[/tex] and [tex]\( y = 4 \)[/tex].
The key point to consider is that for [tex]\( x = 2 \)[/tex], there are two different [tex]\( y \)[/tex]-values (1 and 4). According to the definition of a function, each [tex]\( x \)[/tex]-value must correspond to exactly one [tex]\( y \)[/tex]-value. Since [tex]\( x = 2 \)[/tex] maps to two different [tex]\( y \)[/tex]-values, this violates the definition of a function.
As a result, the table does not represent a function.
Therefore, the correct answer is:
[tex]\[ \text{D. No, because one } x\text{-value corresponds to two different } y\text{-values.} \][/tex]
Given 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]
Let's examine each pair of values:
1. For [tex]\( x = 2 \)[/tex], we have two corresponding [tex]\( y \)[/tex]-values: [tex]\( y = 1 \)[/tex] and [tex]\( y = 4 \)[/tex].
The key point to consider is that for [tex]\( x = 2 \)[/tex], there are two different [tex]\( y \)[/tex]-values (1 and 4). According to the definition of a function, each [tex]\( x \)[/tex]-value must correspond to exactly one [tex]\( y \)[/tex]-value. Since [tex]\( x = 2 \)[/tex] maps to two different [tex]\( y \)[/tex]-values, this violates the definition of a function.
As a result, the table does not represent a function.
Therefore, the correct answer is:
[tex]\[ \text{D. No, because one } x\text{-value corresponds to two different } y\text{-values.} \][/tex]
