End Behavior

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What is end behavior in mathematics?

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End behavior describes the behavior of a function as the input values approach positive or negative infinity.

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What does it mean if a function approaches infinity as x approaches negative infinity?

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It means that as the input values decrease without bound, the output values of the function increase without bound.

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What does it mean if a function approaches negative infinity as x approaches positive infinity?

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It means that as the input values increase without bound, the output values of the function decrease without bound.

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How can you determine the end behavior of a rational function?

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Analyze the degrees of the numerator and denominator. The end behavior is influenced by the leading terms.

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What is the significance of the leading coefficient in determining end behavior?

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The leading coefficient indicates whether the function will rise or fall as x approaches infinity or negative infinity.