Relations and Functions

Front

What is a relation in mathematics?

Back

A relation is a set of ordered pairs, where each pair consists of an input (or domain) and an output (or range).

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What is a function?

Back

A function is a special type of relation where each input is associated with exactly one output.

Front

How can you determine if a relation is a function?

Back

A relation is a function if no two ordered pairs have the same first element (input) with different second elements (outputs).

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (first elements) 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 (second elements) that the function can produce.

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What does it mean for a relation to be one-to-one?

Back

A one-to-one relation is a function where each output is associated with exactly one input, meaning no two different inputs produce the same output.

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What is the vertical line test?

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The vertical line test is a method used to determine if a relation is a function by checking if any vertical line intersects the graph of the relation at more than one point.

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Can a function have the same output for different inputs?

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Yes, a function can have the same output for different inputs, but it cannot have the same input associated with different outputs.

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What is an example of a function?

Back

An example of a function is f(x) = x^2, where each input x has a unique output x^2.

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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 is associated with two different outputs.