Domain, Range, and Functions

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What is a function?

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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) 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 the range of a function from its graph?

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The range can be determined by identifying the lowest and highest points on the graph and the corresponding y-values.

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What does it mean for a relation to be a function?

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A relation is a function if every input (x-value) is associated with exactly one output (y-value).

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108 bananas are left after 7 hours.

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The range is all real numbers since it is a linear function.

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The range is all real numbers greater than or equal to 0, or [0, ∞).

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How can you express the range of a function using set notation?

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The range can be expressed in set notation, for example, {y | -6 ≤ y ≤ 3}.

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What is the difference between open and closed intervals?

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A closed interval includes its endpoints (e.g., [a, b]), while an open interval does not (e.g., (a, b)).