End Behavior of Functions

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What is the end behavior of a function?

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The end behavior of a function describes how the function behaves as the input values approach positive or negative infinity.

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Define the term 'leading term' in a polynomial function.

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The leading term of a polynomial function is the term with the highest degree, which determines the end behavior of the function.

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What does it mean if a polynomial function has an even degree?

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What does it mean if a polynomial function has an odd degree?

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

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The leading coefficient indicates the direction of the end behavior: if it is positive, the function will approach positive infinity in both directions for even degrees, and if it is negative, it will approach negative infinity.

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How can you use a graph to determine end behavior?

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By observing the direction in which the graph extends as it moves towards the left and right ends, you can determine the end behavior of the function.

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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 the function's values increase without bound as the input values decrease.