Identifying Functions

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What is a function in mathematics?

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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 graph represents a function?

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A graph represents a function if any vertical line drawn through the graph intersects it at most once (Vertical Line Test).

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What is the Vertical Line Test?

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The Vertical Line Test is a method to determine if a curve is a graph of a function. If a vertical line intersects the graph more than once, then the graph is not a function.

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

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A relation is 'not a function' if at least one input is associated with more than one output.

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What is an example of a function?

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

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

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

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What is a one-to-one function?

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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 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 definition of a 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 definition of a 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.