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

Quizplus · Accepted Answer

For large negative values of x, the dominant term in the polynomial is 7x^5, which is negative, and hence the function goes in a downward direction. 
Similarly, for large positive values of x, the dominant term is again 7x^5, which has a positive coefficient, and hence the function goes in an upward direction. Therefore, the graph of the function falls to the left and 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 $q ( x ) = 7 x ^ { 5 } + x ^ { 3 } + 7$