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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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. For example, if the leading term is positive and has an even degree, the function will approach positive infinity as x approaches both positive and 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.

Tags

CCSS.HSF-IF.C.7E

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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. A positive leading coefficient means the function will rise to positive infinity, while a negative leading coefficient means it will fall to negative infinity.

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

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You can analyze the graph of the function to see the direction it heads as x approaches positive or negative infinity.

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

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Tags

CCSS.HSF-IF.C.7D