Saturday 12-14-2024 Relations, Functions, Domain, & Range

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What is a function?

Back

A function is a relation that assigns exactly one output (y) for each input (x).

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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) 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) that the function can produce.

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How do you find the value of a function at a specific point?

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To find the value of a function at a specific point, substitute the input value into the function's equation.

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What is the notation for domain in set builder form?

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The notation for domain in set builder form is {x | condition}, where 'condition' describes the values of x.

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What is the notation for range in set builder form?

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The notation for range in set builder form is {y | condition}, where 'condition' describes the values of y.

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What does it mean if a function's range is limited to a specific interval?

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If a function's range is limited to a specific interval, it means that the output values (y) can only take on values within that interval.

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What is the difference between open and closed intervals?

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An open interval (a, b) does not include the endpoints a and b, while a closed interval [a, b] includes both endpoints.

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How do you express a range using interval notation?

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A range can be expressed in interval notation using brackets for closed intervals and parentheses for open intervals, e.g., [a, b) or (a, b].

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What is the significance of the vertical line test?

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The vertical line test is used to determine if a relation is a function; if a vertical line intersects the graph at more than one point, it is not a function.