Function or Not a Function

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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 x-value, there is one and only one corresponding y-value.

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How can you determine if a relation is a function using the vertical line test?

Back

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

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What does it mean if a relation is not a function?

Back

It means that at least one input is associated with multiple outputs.

Front

What is an example of a function?

Back

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

Front

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

Back

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

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What is the definition of 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.

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What is the definition of 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 the significance of the domain in a function?

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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 the significance of the range in a function?

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

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How can you represent a function using a mapping diagram?

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A mapping diagram visually shows how each element of the domain is paired with an element of the range, illustrating the relationship between inputs and outputs.