Describe the end behavior of the polynomial function by finding
-$$f ( x ) = - 7 x ^ { 2 } + 4 x ^ { 3 } + 2 x - 8$$
A) $\infty , -\infty$
B) $-\infty , -\infty$
C) $\infty , \infty$
D) $-\infty , \infty$

Question

Describe the end behavior of the polynomial function by finding 
-$$f ( x ) = - 7 x ^ { 2 } + 4 x ^ { 3 } + 2 x - 8$$
A) $\infty , -\infty$ 
B) $-\infty , -\infty$ 
C) $\infty , \infty$ 
D) $-\infty , \infty$

Quizplus · Accepted Answer

The leading coefficient of the polynomial is positive, so the graph of the function will open upward. The degree of the polynomial is 3, which is odd, so the graph of the function will have no horizontal asymptotes. Therefore, the vertical asymptotes are the only possible end behaviors.

Describe the End Behavior of the Polynomial Function by Finding f(x)=−7x2+4x3+2x−8f ( x ) = - 7 x ^ { 2 } + 4 x ^ { 3 } + 2 x - 8f(x)=−7x2+4x3+2x−8

Describe the End Behavior of the Polynomial Function by Finding $f ( x ) = - 7 x ^ { 2 } + 4 x ^ { 3 } + 2 x - 8$