Interpretting Functions: Understanding Functions, Domain, and Range (CCSS.F-IF.1)
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Common Core High School Functions › Interpretting Functions: Understanding Functions, Domain, and Range (CCSS.F-IF.1)
Consider the relation with domain elements $a,b,c$ and outputs labeled \$1,2,3$ where arrows go $a\to 1$, $b\to 2$, and $c\to 2$. Is this relation a function?
Yes; each input has exactly one output.
No; one input maps to two outputs.
No; two inputs share the same output.
Yes; each output has exactly one input.
Explanation
It is a function because each input ($a$, $b$, and $c$) has exactly one output. Having two different inputs map to the same output (both $b$ and $c$ mapping to 2) is allowed. A relation would fail to be a function only if some input had two outputs or no output.
A school assigns lockers to students. Think of a relation from students (inputs) to lockers (outputs). Which description represents a function?
One student is assigned two different lockers.
Some students are not assigned any locker.
Each student is assigned exactly one locker; two different students may share the same locker.
Some students have two lockers and others have none.
Explanation
A function requires exactly one output for each input. Choice C meets this rule: every student has one locker, and multiple students sharing a locker is allowed. The other choices violate the one-output-per-input rule or leave some inputs without outputs.