Question

Which of the following describes the polynomial function?

Answer 1

Answer: the function has an odd degree.

Explanation:

1) The leading coefficient is the coefficient of the leading term. The leading term is the the term with the highest degree.

The leading term is dominant when x grows. So, for x → infinity the value of a polynomial trends toward infinity if the leading coefficient is positive and toward negative infinity if the leading coefficient is negative.

The graph shows that the function goes to infinity as x grows, so the leading coefficient is positive, which discards the first choice (that the function has a negative leading coefficient).

2) It is right that the polynomial has an odd degree.

The degree of a polynomial is the highest degree of its individual terms.

Odd-degree polynomials have ends that head off in opposite directions, while the ends of even-degree polynomilas come in and leave out the same quadrant.

It is easy to remember is you think that even-degree polynomials behave, on their ends, like quadratics, and all odd-degree polynomials behave, on their ends, like cubics.
3) The other statements are easy to discard: there are two turns on the graph and the function has 3 x-intercepts.