1 Suppose a polynomial function has degree n and leading coe

1. Suppose a polynomial function has degree n and leading coefficient c.

Complete the following statements.

A. The number of turning points is at most__________.

B.If n is odd and c>0, then y approaches __________ as x approaches infinity and y approaches __________ as x approaches negative infinity.

C. If n is odd and c<0, then y approaches __________ as x approaches infinity and y approaches __________ as x approaches negative infinity.

D.If n is even and c>0, then y approaches __________ as x approaches infinity and y approaches __________ as x approaches negative infinity.

E. If n is even and c<0, then y approaches __________ as x approaches infinity and y approaches __________ as x approaches negative infinity.

Solution

1.Here degree is n. And the relationship between turning points and degree is that the turning points is at most n-1 when degree is n

b. Degree is odd and leading coefficient is positive.In this case as x approaches - infinity y approaches to - infinity and as x approaches infinity y approaches to infinity

C.Here degree is odd and leading coefficient is negative.In this case ax x approaches infinity y appoaches to infinity and as x approaches to - infinity y approaches to infinity

D.Here degree is even and leading coefficient is positive.In this case as x approaches negative infinity y approaches to infinity and as x approaches to infinity y approaches to infinity

E.Here degree is even and leading coefficient is negative and in this case as x approaches to negative infinity y approaches to infinity and as x approaches to infinity y approaches to negative infinity