Function or Non-Function?

Front

What is a function in mathematics?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

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How can you determine if a relation is a function?

Back

A relation is a function if every input (x-value) has exactly one output (y-value). This can be checked using the vertical line test on a graph.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a graph of a function. If any vertical line intersects the graph at more than one point, then the relation is not a function.

Front

What is the domain of a function?

Back

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 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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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 function?

Back

An example of a function is f(x) = 2x + 3, where for each value of x, there is a unique value of f(x).

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What is an example of a non-function?

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An example of a non-function is the relation defined by the equation x^2 + y^2 = 1, which can produce multiple y-values for a single x-value.

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What is a one-to-one function?

Back

A one-to-one function is a function where each output is related to exactly one input, meaning no two different inputs produce the same output.

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What is a many-to-one function?

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A many-to-one function is a function where multiple inputs can produce the same output.