What is a Function?

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input.

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How can you determine if a set of ordered pairs is a function?

Back

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

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What is the vertical line test?

Back

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

Front

What is the definition of a relation?

Back

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

Front

What does it mean for a relation to be one-to-one?

Back

A one-to-one relation is a type of function where each input is paired with a unique output, and no two inputs share the same output.

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 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 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 is paired with two different outputs.

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What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input is associated with exactly one output, while a relation can have multiple outputs for a single input.

Front

What is a mapping in the context of functions?

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A mapping is a way to describe how each element in a set (domain) is paired with elements in another set (range).