To determine whether a given relation is a function, we need to verify if every input [tex]\( x \)[/tex] maps to exactly one output [tex]\( y \)[/tex]. In other words, in the context of a table or set of ordered pairs, each [tex]\( x \)[/tex] value should correspond to one and only one [tex]\( y \)[/tex] value.
Let's examine the table with this criterion:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
15 & 4 \\
\hline
12 & 16 \\
\hline
18 & 10 \\
\hline
12 & 3 \\
\hline
\end{array}
\][/tex]
1. For [tex]\( x = 15 \)[/tex], the [tex]\( y \)[/tex] value is 4.
2. For [tex]\( x = 12 \)[/tex], the [tex]\( y \)[/tex] value appears twice: once with [tex]\( y = 16 \)[/tex] and once with [tex]\( y = 3 \)[/tex].
3. For [tex]\( x = 18 \)[/tex], the [tex]\( y \)[/tex] value is 10.
We observe that the [tex]\( x \)[/tex] value of 12 maps to two different [tex]\( y \)[/tex] values: 16 and 3. This means that for the input [tex]\( x = 12 \)[/tex], the output is not unique, violating the definition of a function.
Therefore, this relation is not a function.
Answer:
no
