Question

The function p(x) is an odd degree polynomial with a negative leading coefficient. If q(x) = x3 + 5x2 - 9x - 45, which statement is true?
As x approaches negative infinity, p(x) approaches positive infinity and q(x) approaches negative infinity.


As x approaches negative infinity, p(x) and q(x) approach positive infinity.


As x approaches negative infinity, p(x) and q(x) approach negative infinity.


As x approaches negative infinity, p(x) approaches negative infinity and q(x) approaches positive infinity.

Answer 1

Answer:

A.  As x approaches negative infinity, p(x) approaches positive infinity and q(x) approaches negative infinity.

Step-by-step explanation:

Answer 2

As x approaches negative infinity, p(x) approaches positive infinity and q(x) approaches negative infinity. The function q(x) given is an odd degree polynomial with a positive leading coefficient. Because odd degree polynomials preserve the sign of the value of x, and because the leading coefficients of both functions p(x) and q(x) are of opposite signs, they will diverge to opposite infinities as x approaches infinity. So let's look at the options and see what makes sense. As x approaches negative infinity, p(x) approaches positive infinity and q(x) approaches negative infinity. * OK. This has p(x) and q(x) going to different infinities. Negative infinity to an odd power will result in a negative infinity. And since q(x) has a positive leading coefficient, that means that q(x) will approach negative infinity. Everything here matches, so this is the correct choice. As x approaches negative infinity, p(x) and q(x) approach positive infinity. * This is claiming that p(x) and q(x) are approaching the same infinity. So we immediately know this is the wrong choice, given what I said earlier about those functions. As x approaches negative infinity, p(x) and q(x) approach negative infinity. * This is claiming that p(x) and q(x) are approaching the same infinity. So we immediately know this is the wrong choice, given what I said earlier about those functions. As x approaches negative infinity, p(x) approaches negative infinity and q(x) approaches positive infinity. * OK. This has p(x) and q(x) going to different infinities. Negative infinity to an odd power will result in a negative infinity. And since q(x) has a positive leading coefficient, that means that q(x) will approach negative infinity. But this option is claiming that q(x) is going to positive infinity. That's wrong and therefore this choice is wrong.