3-1: Is a Relation a Function?

Front

What is a relation in mathematics?

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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What is a function?

Back

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

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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 (x-value) with different second elements (y-values).

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What does it mean for a relation to NOT be a function?

Back

It means that at least one input (x-value) is associated with more than one output (y-value).

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Give an example of a function using ordered pairs.

Back

(1, 2), (2, 3), (3, 4) is a function because each x-value is unique.

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Give an example of a relation that is NOT a function using ordered pairs.

Back

(1, 2), (1, 3), (2, 4) is NOT a function because the x-value '1' is associated with two different y-values.

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 a mapping diagram?

Back

A mapping diagram visually represents a relation by showing how each input is paired with its output.

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What is the domain of a function?

Back

The domain is the set of all possible input values (x-values) for the function.

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What is the range of a function?

Back

The range is the set of all possible output values (y-values) for the function.