Question
17. Explain how you would determine if a relation is a function given a list of ordered pairs. (2
Solution
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Selena
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Answer
### Check if each input value in the list of ordered pairs maps to exactly one output value. If any input has multiple outputs, the relation is not a function.
Explanation
## Step 1: Unique Inputs Check### A relation is a function if each input value corresponds to exactly one output value. In a set of ordered pairs (representing the relation), examine the first element (input) of each pair. If any input value appears more than once with different output values, the relation is not a function.## Step 2: Illustration with Example### Consider the set of ordered pairs {(1, 2), (2, 4), (3, 6), (1, 8)}. The input '1' appears twice, corresponding to outputs '2' and '8'. Therefore, this relation is not a function. Conversely, {(1,2), (2,4), (3,6)} is a function because each input has a unique output.