End Behavior

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What is end behavior in mathematics?

Back

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

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What does it mean if a function's end behavior is 'up/up'?

Back

It means that as x approaches both negative infinity and positive infinity, the function f(x) approaches positive infinity.

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What does it mean if a function's end behavior is 'down/down'?

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It means that as x approaches both negative infinity and positive infinity, the function f(x) approaches negative infinity.

Front

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

Back

The end behavior of a polynomial function is determined by its leading term, specifically its degree and leading coefficient.

Front

What is the end behavior of a polynomial with an even degree and a positive leading coefficient?

Back

The end behavior is 'up/up', meaning f(x) approaches positive infinity as x approaches both negative and positive infinity.

Front

What is the end behavior of a polynomial with an even degree and a negative leading coefficient?

Back

The end behavior is 'down/down', meaning f(x) approaches negative infinity as x approaches both negative and positive infinity.

Front

What is the end behavior of a polynomial with an odd degree and a positive leading coefficient?

Back

The end behavior is 'down/up', meaning f(x) approaches negative infinity as x approaches negative infinity and positive infinity as x approaches positive infinity.

Front

What is the end behavior of a polynomial with an odd degree and a negative leading coefficient?

Back

The end behavior is 'up/down', meaning f(x) approaches positive infinity as x approaches negative infinity and negative infinity as x approaches positive infinity.

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Back

The end behavior is 'up/up' because the leading term is positive and has an even degree.

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The end behavior is 'up/down' because the leading term is negative and has an odd degree.