To determine whether a given relation represents a function, we need to check if each input value (each [tex]\( x \)[/tex] value) maps to exactly one output value (each [tex]\( y \)[/tex] value).
Let's consider the given relation:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-16 & 17 \\
\hline
8 & 18 \\
\hline
8 & 3 \\
\hline
4 & 11 \\
\hline
\end{array}
\][/tex]
1. Examine all [tex]\( x \)[/tex] values in the relation:
- For [tex]\( x = -16 \)[/tex], the mapped [tex]\( y \)[/tex] is 17.
- For [tex]\( x = 8 \)[/tex], there are two different [tex]\( y \)[/tex] values, 18 and 3.
- For [tex]\( x = 4 \)[/tex], the mapped [tex]\( y \)[/tex] is 11.
2. Identify if there are any duplicate [tex]\( x \)[/tex] values with different [tex]\( y \)[/tex] values:
- The [tex]\( x \)[/tex] value 8 appears twice, with corresponding [tex]\( y \)[/tex] values of 18 and 3. This means the input 8 maps to two different outputs, which violates the definition of a function.
Since the value [tex]\( x = 8 \)[/tex] in the relation maps to two different [tex]\( y \)[/tex] values (18 and 3), this relation does not meet the definition of a function.
Therefore, the answer is no. This relation does not represent a function.
