Behavior of polynomial fct at infinities

Study the behavior of a polynomial fct

Consider f(x)=[math]bx^a[/math][br]Keep b=1 and change the exponent a.[br]What do you notice?[br]Now fix a=1,2,3,... and for each case change b.[br]What do you notice?[br]when you finish answer the questions below.

Behavior at infinity

The curves of all polynomial function with even degrees start and end at

minus infinity plus infinity same ends at different ends

Behavior at infinity

The curves of all polynomial function with odd degrees start and end at

plus infinity at different ends minus infinity same ends

what is the role of the coefficient of the leading term?

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Información: Behavior of polynomial fct at infinities