Functions (general)

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.

Front

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 function. If a vertical line intersects the curve at more than one point, then the curve is not a function.

Front

What does it mean for a set of ordered pairs to represent a function?

Back

A set of ordered pairs represents a function if no two pairs have the same first element (x-value) with different second elements (y-values).

Front

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 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?

Back

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

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What is a domain in the context of functions?

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 a range in the context of functions?

Back

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

Front

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.