Relations, Functions, Domain and Range

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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).

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What is a function?

Back

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

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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 the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) that the function can accept.

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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 (y-values) that the function can produce.

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How do you determine the domain from a graph?

Back

To determine the domain from a graph, identify the x-values that the graph covers.

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How do you determine the range from a graph?

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To determine the range from a graph, identify the y-values that the graph covers.

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

Back

A relation is not a function if at least one input (x-value) is associated with more than one output (y-value).

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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 has a unique y-value.

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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.