Which of the following polynomials has a graph which exhibit

Which of the following polynomials has a graph which exhibits the end behavior of upward to the left and downward to the right? 2. _______ A. f (x) = –5x 4 – x 3 – x 2 – 5 B. f (x) = 2x 3 + 8x 2 – x + 3 C. f (x) = 7x 6 + 3x 2 + x D. f (x) = –6x 3 + 2x 2 – x – 1

Solution

A. f (x) = –5x 4 – x 3 – x 2 – 5

degree is even ,leading coefficient negative

graph exhibits the end behavior of downward to the left and downward to the right

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B. f (x) = 2x 3 + 8x 2 – x + 3

degree is odd ,leading coefficient positive

graph exhibits the end behavior of downward to the left and upward to the right

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C. f (x) = 7x 6 + 3x 2 + x

degree is even ,leading coefficient positive

graph exhibits the end behavior of upward to the left and upward to the right

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D. f (x) = –6x 3 + 2x 2 – x – 1

degree is odd ,leading coefficient negative

graph exhibits the end behavior of upward to the left and downward to the right

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so the answer is D. f (x) = –6x 3 + 2x 2 – x – 1