Function or Non-Function?

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input. In other words, for every input value, there is a unique output value.

Front

What is the vertical line test?

Back

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

Front

What does it mean for a relation to not be a function?

Back

A relation is not a function if there exists at least one input that corresponds to multiple outputs.

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 has only one output.

Front

What is the definition of a relation in mathematics?

Back

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

Front

What is an example of a function?

Back

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

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What is an example of a non-function?

Back

An example of a non-function is the relation {(1, 2), (1, 3)}, where the input 1 corresponds to two different outputs.

Front

What is the difference between a function and a non-function?

Back

The difference is that a function has exactly one output for each input, while a non-function can have multiple outputs for a single input.

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each output is associated with 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.