Functions

Front

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 graph represents a function?

Back

A graph represents a function if any vertical line drawn through the graph intersects it at most once (Vertical Line Test).

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

Back

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?

Back

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

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What does it mean for a function to be defined?

Back

A function is defined when there is a clear rule that assigns exactly one output to each input in its domain.

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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.

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What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where each input x produces 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 the set of points {(1, 2), (1, 3)}, where the input 1 is related to two different outputs.

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What is a vertical line test?

Back

The vertical line test is a method used to determine if a graph represents a function by checking if any vertical line intersects the graph more than once.