Describe the right-hand and the left-hand behavior of the graph of
$q ( x ) = 7 x ^ { 5 } + x ^ { 3 } + 7$.
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 positive, the graph rises to the left and falls to the right.
C) Because the degree is odd and the leading coefficient is positive, 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 positive, the graph rises to the left and rises to the right.

Question

Describe the right-hand and the left-hand behavior of the graph of 
$q ( x ) = 7 x ^ { 5 } + x ^ { 3 } + 7$.
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 positive, the graph rises to the left and falls to the right.
C) Because the degree is odd and the leading coefficient is positive, 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 positive, the graph rises to the left and rises to the right.

Quizplus · Accepted Answer

Because the degree is odd and the leading coefficient is positive, the ends behave in opposite ways. As x approaches negative infinity, q(x) approaches negative infinity (falls to the left). As x approaches positive infinity, q(x) approaches positive infinity (rises to the right).

Describe the Right-Hand and the Left-Hand Behavior of the Graph q(x)=7x5+x3+7q ( x ) = 7 x ^ { 5 } + x ^ { 3 } + 7q(x)=7x5+x3+7

Describe the Right-Hand and the Left-Hand Behavior of the Graph $q ( x ) = 7 x ^ { 5 } + x ^ { 3 } + 7$