Understand functions as mappings from inputs to exactly one output; connect f(x) to graph y=f(x).
Decide whether an ordered-pair set represents a function
Problem
For the relation \({(1,~3),~(2,~5),~(3,~5)}\), determine whether it is a function and cite supporting input-output evidence.
Big Picture
What this problem is really about
Function status is controlled by the first coordinates, since those are the inputs. We’ll scan the relation input by input and look for a single input paired with two different outputs; that would be the decisive conflict. Repeated outputs alone are allowed because different inputs may lead to the same value.
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