Functions, Functions, Functions

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What is a function?

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A function is a relation that assigns exactly one output (y-value) for each input (x-value).

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What is the definition of the domain of 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 the range of 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 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 does it mean if a relation is not a function?

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A relation is not a function if at least one input (x-value) is associated with more than one output (y-value).

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What is the significance of the x-values in a function?

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The x-values in a function are the inputs, which determine the corresponding y-values (outputs).

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What is the significance of the y-values in a function?

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The y-values in a function are the outputs, which result from applying the function to the x-values (inputs).

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What is an example of a function?

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An example of a function is f(x) = 2x + 3, where each x-value has a unique corresponding y-value.

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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 {(1, 2), (1, 3)}, where the input 1 has two different outputs.

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What is the notation used to represent the domain of a function?

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The domain of a function is often represented using the notation D: {x | x is in the set of inputs}.