Function, Relations, Domain,and Range

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What is a function?

Back

A function is a relation in which each input (or domain element) is associated with exactly one output (or range element).

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What is a relation?

Back

A relation is a set of ordered pairs, where each pair consists of an input and an output.

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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?

Back

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 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 does it mean if a graph is not a function?

Back

If a graph is not a function, it means that at least one input value is associated with more than one output value.

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What is the difference between a function and a non-function?

Back

A function has a unique output for each input, while a non-function has at least one input that corresponds to multiple outputs.

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What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where each x-value has a unique y-value.

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What is an example of a non-function?

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An example of a non-function is the relation {(1, 2), (1, 3)}, where the input 1 corresponds to two different outputs.

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What is the significance of the domain and range in a function?

Back

The domain and range define the limits of the function's inputs and outputs, respectively, and are essential for understanding its behavior.