# Video: Understanding Functions

Which of the following is the best description for a function? [A] A function is a mathematical rule that assigns to each input more than one output. [B] A function is a relation such that every input is mapped to multiple outputs. [C] A function is a relation that assigns to each input exactly one output.

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### Video Transcript

Which of the following is the best description for a function? A) A function is a mathematical rule that assigns to each input more than one output. B) A function is a relation such that every input is mapped to multiple outputs. Or C) A function is a relation that assigns to each input exactly one output.

Let’s consider each of these statements. Option A says “a function is a mathematical rule that assigns to each input more than one output.” We could visualize it like this. But based on the given information, if we input 𝑥, some value, we get out more than one output. We could get 𝑦, 𝑧. Here, the 𝑥, 𝑦, and 𝑧 are just placeholders for other values because we don’t know anything else about this rule.

How then would we visualize option B, “a function is a relation such that every input is mapped to multiple outputs?” We could look at option B like this. And again, we see that every input is mapped to multiple outputs. We’ll do the same thing to visualize option C. We have a relation that assigns input to output. But in this case, each input has only one output. And this relationship where each input relates to exactly one output most closely represents the definition of a function. A function relates an input to an output. It does not relate one input to multiple outputs. And so we choose option C.