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What is a function in mathematical terms?

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.

Tags

CCSS.8.F.A.1

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How can you determine if a relation is a function?

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A relation is a function if every input (x-value) has exactly one output (y-value). This can be checked using the vertical line test on a graph.

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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 a vertical line intersects the curve at more than one point, then the curve is not a function.

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What does it mean for a relation to not be a function?

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A relation is not a function if at least one input is associated with more than one output.

Tags

CCSS.8.F.A.1

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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, as long as each input corresponds to only one output.

Tags

CCSS.8.F.A.1

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What is a one-to-one function?

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

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What is a many-to-one function?

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A many-to-one function is a function where multiple inputs can produce the same output.

Tags

CCSS.8.F.A.1

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What is a one-to-many relation?

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A one-to-many relation is not a function because a single input is associated with multiple outputs.

Tags

CCSS.8.F.A.1

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What is the domain of a function?

Back

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

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What is the range of a function?

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The range of a function is the set of all possible output values (y-values) that the function can produce.