Functions

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What is a function?

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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What is the domain of a function?

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The domain of a function is the set of all possible input values (x-values) that the function can accept.

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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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How can you determine if a set of ordered pairs is a function?

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A set of ordered pairs is a function if no two different pairs have the same first element (x-value).

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What does it mean for a graph to represent a function?

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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 Vertical Line Test?

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The Vertical Line Test is a method to determine if a graph is a function by checking if any vertical line crosses the graph more than once.

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What is a mapping diagram?

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A mapping diagram visually represents a function by showing how each input is paired with an output.

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What is an example of a function?

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An example of a function is f(x) = 2x + 3, where each input x 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)}, where the input 1 is paired with two different outputs.

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What does it mean if a function is one-to-one?

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