End Behavior of Polynomials

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What is the end behavior of a polynomial function?

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The end behavior of a polynomial function describes how the function behaves as the input values (x) approach positive or negative infinity. It is determined by the degree and leading coefficient of the polynomial.

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Define the degree of a polynomial.

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The degree of a polynomial is the highest power of the variable (x) in the polynomial expression. It indicates the polynomial's overall behavior and the number of roots it can have.

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What is a leading coefficient?

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The leading coefficient is the coefficient of the term with the highest degree in a polynomial. It influences the direction of the polynomial's end behavior.

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How does the leading coefficient affect end behavior for even-degree polynomials?

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For even-degree polynomials, if the leading coefficient is positive, both ends of the graph rise to positive infinity. If it is negative, both ends fall to negative infinity.

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How does the leading coefficient affect end behavior for odd-degree polynomials?

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For odd-degree polynomials, if the leading coefficient is positive, the left end falls to negative infinity and the right end rises to positive infinity. If it is negative, the left end rises to positive infinity and the right end falls to negative infinity.

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The degree is 5 and the leading coefficient is 4 (positive).

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As @@x ightarrow ext{infinity}, f(x) ightarrow - ext{infinity}@@.

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If a polynomial has a degree of 3 and a negative leading coefficient, what is its end behavior?

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