Functions (general)

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What is a function in mathematics?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

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How can you determine if a relation is a function?

Back

A relation is a function if no two ordered pairs have the same first element (input) with different second elements (outputs).

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What is the vertical line test?

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The vertical line test is a method to determine if a curve is a function. If any vertical line intersects the curve more than once, then the curve is not a function.

Front

What does it mean for a set of ordered pairs to represent a function?

Back

It means that each first element (input) in the ordered pairs corresponds to exactly one second element (output).

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Can a function have the same output for different inputs?

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Yes, a function can have the same output for different inputs, but each input must map to only one output.

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What is an example of a function?

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An example of a function is the relation {(1, 2), (2, 3), (3, 4)} where each input has a unique output.

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What is an example of a relation that is not a function?

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An example of a relation that is not a function is {(1, 2), (1, 3)} because the input '1' corresponds to two different outputs.

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What is the definition of a one-to-one function?

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A one-to-one function is a function where each output is related to exactly one input, meaning no two different inputs produce the same output.

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What is the difference between a function and a relation?

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A function is a specific type of relation where each input is associated with exactly one output, while a relation can have multiple outputs for a single input.

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What is a domain in the context of functions?

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The domain of a function is the set of all possible input values (x-values) for which the function is defined.