AP Precalculus – Rational Functions: End Behavior & Zeros – Drill 6

About This Drill

AP Precalculus – Rational Functions: End Behavior & Zeros – Drill 6 is a Math practice drill covering Rational Functions: End Behavior & Zeros. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.

This AP® Precalculus drill covers rational functions — specifically end behavior determined by comparing degrees of numerator and denominator, and identifying zeros from the numerator. Practice distinguishing horizontal asymptotes, zeros, and the role of sign analysis in rational functions.

Questions in This Drill

1. What is the horizontal asymptote of \( f(x) = \dfrac{4x^3 - 2x + 1}{2x^3 + 5x^2 - 3} \)?
2. Which of the following gives all real zeros of \( g(x) = \dfrac{(x-3)(x+1)(x-5)}{(x+4)(x-3)} \)?
3. The concentration C (in milligrams per liter) of a medication in the bloodstream t hours after administration is modeled by \( C(t) = \dfrac{8t}{t^2 + 4} \) for t ≥ 0. What does the end behavior of this model indicate about the concentration as t → ∞?
4. Let \( r(x) = \dfrac{x^2 - 4x - 5}{x^2 - x - 20} \). On which of the following intervals is r(x) < 0?
5. A student claims: "For any rational function \( r(x) = \dfrac{p(x)}{q(x)} \), if the degree of p(x) is greater than the degree of q(x), then r(x) has no horizontal asymptote and therefore \( \lim_{x \to \infty} r(x) \) does not exist." Which of the following best evaluates this claim?