Functions and Relations

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. In other words, for every input value, there is a unique output value.

Front

What is a relation?

Back

A relation is a set of ordered pairs, where each pair consists of an input and an output. It can have multiple outputs for a single input.

Front

How can you determine if a mapping is a function?

Back

A mapping is a function if no input value is associated with more than one output value.

Front

What does it mean if a table represents a function?

Back

A table represents a function if each input value corresponds to exactly one output value.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function. If a vertical line intersects the graph at more than one point, it is not a function.

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What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where each input x has a unique output.

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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 has two different outputs.

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What is a one-to-one function?

Back

A one-to-one function 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 a many-to-one function?

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A many-to-one function is a function where multiple inputs can produce the same output.

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What is a domain in 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.