Functions and Notation

Front

What is a function?

Back

A function is a relation where every input (x-value) has exactly one output (y-value).

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What does the vertical line test determine?

Back

The vertical line test determines 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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Front

What is the definition of a relation?

Back

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

Front

Can a function have multiple outputs for a single input?

Back

No, a function cannot have multiple outputs for a single input; each input must correspond to exactly one output.

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What is an example of a non-function?

Back

A relation where an input has two or more outputs, such as the pairs {(1, 2), (1, 3)}.

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What does it mean for a function to be defined?

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A function is defined when there is a clear rule that assigns exactly one output to each input.

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What is the domain of a function?

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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?

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