Relations and Functions

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What is a relation in mathematics?

Back

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

Tags

CCSS.8.F.A.1

Front

What defines a function?

Back

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

Tags

CCSS.8.F.A.1

Front

What is the domain of a function?

Back

The domain 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?

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The range is the set of all possible output values (y-values) that a function can produce.

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How can you determine if a relation is a function?

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

Tags

CCSS.8.F.A.1

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What is a one-to-one function?

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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 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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What is an example of a function?

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An example of a function is f(x) = 2x + 3, where each x-value corresponds to exactly one y-value.

Tags

CCSS.8.F.A.1

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What is an example of a relation that is not a function?

Back

An example of a relation that is not a function is {(1, 2), (1, 3)}, where the input 1 corresponds to two different outputs.

Tags

CCSS.8.F.A.1

Front

What is the difference between a function and a relation?

Back

The difference is that all functions are relations, but not all relations are functions; functions have a unique output for each input.

Tags

CCSS.8.F.A.1