Functions, Domain and Range

Front

What is a function?

Back

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?

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 do you find the domain of a function?

Back

To find the domain, identify the values of x that make the function undefined, such as division by zero or square roots of negative numbers.

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

Back

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

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What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where for every x, there is a unique y.

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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 input 1 corresponds to two different outputs.

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What is the notation for domain?

Back

The domain is often expressed in interval notation, such as (-∞, +∞) or [0, +∞).

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What is the notation for range?

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The range is also expressed in interval notation, such as (-2, 10] or [3, 8).

Front

How do you express the domain of f(x) = 1/(x-2)?

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The domain is all real numbers except x = 2, expressed as (-∞, 2) ∪ (2, +∞).