Relations, Functions, Domain, Range

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What is a relation in mathematics?

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A relation is a set of ordered pairs, where each pair consists of an input (x-value) and an output (y-value).

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What is a function?

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A function is a special type of relation where each input (x-value) is associated with exactly one output (y-value).

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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 can you determine if a relation is a function?

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A relation is a function if no x-value is paired with more than one y-value.

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What does it mean for a function to be defined on a specific interval?

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It means that the function only takes input values (x-values) within that interval.

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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 x-value corresponds to one y-value.

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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 x-value 1 is paired with two different y-values.

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What is the notation for domain?

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The notation for domain can be expressed in interval notation, such as (-∞, ∞) or using inequalities like x > -3.

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What is the notation for range?

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The notation for range can also be expressed in interval notation, such as [0, 4] or using set notation like {y | y ≥ 0}.