End Behavior

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What is end behavior in polynomial functions?

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End behavior describes the behavior of a polynomial function as the input values (x) approach 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 is determined by the leading term of the polynomial, specifically its degree and leading coefficient.

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

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If a polynomial has an odd degree, its end behavior will be opposite in the two directions: as x approaches infinity, f(x) approaches infinity, and as x approaches negative infinity, f(x) approaches negative infinity.

Front

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

Back

If a polynomial has an even degree, its end behavior will be the same in both directions: as x approaches infinity, f(x) approaches infinity, and as x approaches negative infinity, f(x) also approaches infinity.

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial.

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How does the leading coefficient affect end behavior?

Back

If the leading coefficient is positive, the end behavior will rise to infinity in the direction of the leading term's degree. If it is negative, the end behavior will fall to negative infinity.

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Front

What does @@x ightarrow - ext{∞}@@ signify?

Back

It signifies that x is approaching negative infinity.