Functions

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 mapping is a function?

Back

A mapping is a function if every input (x value) corresponds to exactly one output (y value). If any input has multiple outputs, it is not a function.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a function. If any vertical line intersects the curve more than once, the curve 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.

Front

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.

Front

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.

Front

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.

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What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where each input x produces a unique output.

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What is an example of a relation that is not a function?

Back

An example of a relation that is not a function is {(1, 2), (1, 3)}, where the input 1 corresponds to two different outputs.

Front

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 for each input in its domain.