Functions & Relations/ Domain & Range

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What is a function in mathematical terms?

Back

A function is a relation that assigns exactly one output (y-value) for each input (x-value).

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What is the definition of 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.

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What is the definition of range in 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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What does the vertical line test determine?

Back

The vertical line test determines whether a graph represents a function. If any vertical line intersects the graph at more than one point, it is not a function.

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What is a mapping in the context of functions?

Back

A mapping is a way to describe how each element of a set (domain) is paired with an element of another set (range).

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What is the difference between a function and a relation?

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A function is a specific type of relation where each input is associated with exactly one output, while a relation can have multiple outputs for a single input.

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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 corresponding 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.

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How can you identify a function from a set of ordered pairs?

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To identify a function from a set of ordered pairs, check that no x-value is repeated with different y-values.

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What is the significance of the output values in a function?

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The output values (y-values) indicate the results of applying the function to the input values (x-values).