Describe the right-hand and the left-hand behavior of the graph of $t ( x ) = - \frac { 4 } { 7 } \left( x ^ { 3 } + 5 x ^ { 2 } + 8 x + 1 \right)$.
A) Because the degree is odd and the leading coefficient is positive, the graph falls to the left and falls to the right.
B) Because the degree is odd and the leading coefficient is negative, the graph rises to the left and falls to the right.
C) Because the degree is odd and the leading coefficient is negative, the graph falls to the left and rises to the right.
D) Because the degree is odd and the leading coefficient is positive, the graph rises to the left and rises to the right.
E) Because the degree is even and the leading coefficient is negative, the graph rises to the left and falls to the right.

Question

Quizplus · Accepted Answer

Because the degree of the polynomial is odd and the leading coefficient is negative, the graph rises to the left and falls to the right according to the end behavior theorem.

Describe the Right-Hand and the Left-Hand Behavior of the Graph t(x)=−47(x3+5x2+8x+1)t ( x ) = - \frac { 4 } { 7 } \left( x ^ { 3 } + 5 x ^ { 2 } + 8 x + 1 \right)t(x)=−74​(x3+5x2+8x+1)

Describe the Right-Hand and the Left-Hand Behavior of the Graph $t ( x ) = - \frac { 4 } { 7 } \left( x ^ { 3 } + 5 x ^ { 2 } + 8 x + 1 \right)$