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? A. As x approaches negative infinity, p (x) approaches positive infinity and q (x) approaches negative infinity. B. As x approaches negative infinity, p (x) and q (x) approach positive infinity. C. As x approaches negative infinity, p (x) and q (x) approach negative infinity. D. As x approaches negative infinity, p (x) approaches negative infinity and q (x) approaches positive infinity.

Question

Mathematics

Ignacio Mcgee

29 December, 06:44

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? A. As x approaches negative infinity, p (x) approaches positive infinity and q (x) approaches negative infinity. B. As x approaches negative infinity, p (x) and q (x) approach positive infinity. C. As x approaches negative infinity, p (x) and q (x) approach negative infinity. D. As x approaches negative infinity, p (x) approaches negative infinity and q (x) approaches positive infinity.

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Hudson Ponce · Answer 1

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

Step-by-step explanation:

The order of the polynomial and the sign of the leading coefficient will let us find the correct answer easily,

If you get a negative number (such as negative infinity) and you take it to an odd power, (for example 3), you will still get a negative number.

As q (x) has a positive leading coefficient, this means that as x approaches negative infinity, q (x) will approach too negative infinity.

Since p (x) has an odd degree, but negative leading coefficient,

(-) * (-) = +

And this means that p (x) approaches positive infinity