Identify Functions

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What is a function?

Back

A function is a relation that assigns exactly one output for each input. In other words, for every x-value, there is one and only one y-value.

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What is a relation?

Back

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

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How can you determine if a mapping is a function?

Back

A mapping is a function if no two ordered pairs have the same first element (x-value) with different second elements (y-values).

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What does it mean for a set of ordered pairs to be a function?

Back

A set of ordered pairs is a function if each x-value is paired with exactly one y-value.

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What is the vertical line test?

Back

The vertical line test is a method used 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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Can a function have the same output for different inputs?

Back

Yes, a function can have the same output for different inputs. For example, f(2) = 5 and f(3) = 5 are valid in 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)}, because the input 1 is associated with two different outputs.

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What does it mean if a relation is not a function?

Back

If a relation is not a function, it means that at least one input is associated with more than one output.

Front

What is the definition of a one-to-one function?

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