End Behavior of Functions

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What is end behavior of a function?

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End behavior describes how the values of a function behave as the input approaches positive or negative infinity.

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What does it mean if a function approaches -∞ as x approaches -∞?

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

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What does it mean if a function approaches +∞ as x approaches +∞?

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

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

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The end behavior of a polynomial function is determined by its leading term. The sign and degree of the leading term dictate whether the function goes to +∞ or -∞ as x approaches ±∞.

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What does it mean if a function approaches +∞ as x approaches -∞?

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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 is the significance of the degree of a polynomial in determining end behavior?

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The degree of a polynomial indicates the highest power of x, which influences the end behavior; even-degree polynomials have the same end behavior on both sides, while odd-degree polynomials have opposite end behaviors.