functions and evaluating function

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What is a function?

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A function is a relation that assigns exactly one output for each input from its domain.

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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) 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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How do you determine if a relation is a function?

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A relation is a function if each input is associated with exactly one output. This can be checked using the vertical line test.

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What is the vertical line test?

Back

The vertical line test states that if a vertical line intersects a graph at more than one point, then the graph does not represent a function.

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What does it mean for a mapping to be 'not a function'?

Back

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

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What is an example of a function?

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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 associated with two different outputs.

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What is the significance of the ordered pairs in a function?

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Ordered pairs in a function represent the relationship between inputs and outputs, where the first element is the input and the second is the output.