To determine whether the given relation is a function, we need to check if every input (first element in each ordered pair) in the relation corresponds to exactly one output (second element in each ordered pair). If any input maps to more than one output, the relation is not a function.
Given the relation:
[tex]\[
\{(3,2),(3,-2),(1,-4),(-1,2)\}
\][/tex]
Let's examine each ordered pair:
1. The first pair is \((3,2)\) which maps the input \(3\) to the output \(2\).
2. The second pair is \((3,-2)\) which maps the input \(3\) to the output \(-2\).
We see that the input \(3\) maps to two different outputs: \(2\) and \(-2\). According to the definition of a function, an input must map to exactly one output. Since this condition is violated here, the given relation is not a function.
Therefore, the answer to whether the relation is a function is:
No
