Ortega Todd
05/17/2024 · High School
\[ \text { Relation } 4 \] \[ \{(-7, j),(7, m),(6, j),(7, j)\} \] Function Not a function
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Step-by-step Solution
To determine whether the given relation is a function, we need to check if each input (the first element of each ordered pair) is associated with exactly one output (the second element of each ordered pair).
The given relation is:
\[
\{(-7, j), (7, m), (6, j), (7, j)\}
\]
Now, let's analyze the inputs:
- The input \(-7\) is associated with \(j\).
- The input \(7\) is associated with both \(m\) and \(j\).
- The input \(6\) is associated with \(j\).
Since the input \(7\) has two different outputs (\(m\) and \(j\)), this violates the definition of a function, which states that each input must map to exactly one output.
Therefore, the relation is **not a function**.
Quick Answer
The relation is not a function because one input has two different outputs.
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