End Behavior

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What is end behavior in mathematics?

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End behavior refers to the behavior of a function as the input values approach positive or negative infinity. It describes how the output values of the function behave in these limits.

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

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If a function approaches infinity as @@x ightarrow - ext{infinity}@@, it means that the values of the function increase without bound as the input values decrease.

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

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If a function approaches negative infinity as @@x ightarrow ext{infinity}@@, it means that the values of the function decrease without bound as the input values increase.

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How do you determine the end behavior of a polynomial function?

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To determine the end behavior of a polynomial function, look at the leading term (the term with the highest degree). The sign and degree of this term will dictate the end behavior as x approaches positive and negative infinity.

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What does it mean if a function has a horizontal asymptote?

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A horizontal asymptote indicates the value that a function approaches as x approaches positive or negative infinity. It reflects the end behavior of the function.

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