Function vs Nonfunction

Front

What is a function?

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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What is a non-function?

Back

A non-function is a relation where at least one input is related to more than one output.

Front

How can you determine if a relation is a function?

Back

You can use the vertical line test: if a vertical line intersects the graph of the relation at more than one point, it is not a function.

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What is an example of a function?

Back

An example of a function is f(x) = 2x, where each input x has a unique output.

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What is an example of a non-function?

Back

An example of a non-function is the relation defined by the equation x^2 + y^2 = 1, which relates some x values to multiple y values.

Front

What does the term 'input' refer to in a function?

Back

The input is the value you provide to a function, often represented as x.

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What does the term 'output' refer to in a function?

Back

The output is the value that results from applying the function to the input, often represented as f(x) or y.

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Can a function have the same output for different inputs?

Back

Yes, a function can have the same output for different inputs, as long as each input corresponds to only one output.

Front

What is a mapping diagram?

Back

A mapping diagram visually represents a function by showing how each input is paired with its output.

Front

What is the domain of a function?

Back

The domain is the set of all possible inputs (x values) for the function.