End behavior of functions

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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 approach positive or negative infinity. It is determined by the degree of the polynomial and the sign of the leading coefficient.

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How does the degree of a polynomial affect its end behavior?

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The degree of a polynomial determines the number of times the graph can turn. For even degrees, the ends of the graph will either both go up or both go down. For odd degrees, one end will go up and the other will go down.

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

Back

The leading coefficient affects the direction of the ends of the graph. If the leading coefficient is positive, the ends will rise in the same direction; if negative, they will fall in the same direction.

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How do you determine the end behavior from a graph?

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To determine end behavior from a graph, observe the direction in which the graph heads as the x-values approach positive and negative infinity.

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What does it mean if a polynomial has an even degree and a positive leading coefficient?

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What does it mean if a polynomial has an odd degree and a negative leading coefficient?

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If a polynomial has an odd degree and a negative leading coefficient, the left end of the graph will rise while the right end will fall.