Describe the right-hand and the left-hand behavior of the graph of $q ( x ) = - 3 x ^ { 4 } + 7 x ^ { 3 } + 27$ .
A)Because the degree is even and the leading coefficient is negative, the graph falls to the left and falls to the right.
B)Because the degree is even and the leading coefficient is negative, the graph rises to the left and falls to the right.
C)Because the degree is even and the leading coefficient is negative, the graph falls to the left and rises to the right.
D)Because the degree is even and the leading coefficient is negative, the graph rises to the left and rises to the right.
E)Because the degree is odd and the leading coefficient is negative, the graph rises to the left and rises to the right.

Question

Quizplus · Accepted Answer

The degree of the polynomial is 4, which is even, and the leading coefficient is -3, which is negative. This combination means the graph falls (goes down) as x moves towards both positive and negative infinity.

Describe the Right-Hand and the Left-Hand Behavior of the Graph q(x)=−3x4+7x3+27q ( x ) = - 3 x ^ { 4 } + 7 x ^ { 3 } + 27q(x)=−3x4+7x3+27

Describe the Right-Hand and the Left-Hand Behavior of the Graph $q ( x ) = - 3 x ^ { 4 } + 7 x ^ { 3 } + 27$