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

The degree of the polynomial $q(x) = 7x^5 + x^3 + 7$ is 5, which is odd, and the leading coefficient is 7, which is positive. For polynomials with odd degrees and positive leading coefficients, as $x$ approaches negative infinity, the graph falls (decreases), and as $x$ approaches positive infinity, the graph rises (increases).

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 $q ( x ) = 7 x ^ { 5 } + x ^ { 3 } + 7$