AP Precalculus – Polynomial End Behavior – Drill 5

About This Drill

AP Precalculus – Polynomial End Behavior – Drill 5 is a Math practice drill covering Polynomial End Behavior. 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 focuses on polynomial end behavior — using limit notation to describe what happens to a function's output as x approaches positive or negative infinity. Master the role of degree and leading coefficient in determining tail direction.

Questions in This Drill

1. Which of the following correctly describes the end behavior of \( f(x) = -3x^4 + 7x^2 - 2 \)?
2. A polynomial p(x) has the property that \( \lim_{x \to \infty} p(x) = \infty \) and \( \lim_{x \to -\infty} p(x) = -\infty \). Which of the following must be true?
3. The table below shows selected values of a polynomial function g(x).
   
   

   x	−1000	−100	100	1000
   g(x)	8.1 × 108	8.1 × 104	8.1 × 104	8.1 × 108

   
   Based on the table, which statement about the end behavior of g is most consistent with the data?
4. Let f(x) = 2x³ − 5x² + x − 7 and h(x) = −f(x). Which of the following correctly describes the end behavior of h(x)?
5. A scientist models the net population growth rate of a species (in thousands per year) using the polynomial P(t) = −t⁵ + 3t³ + 10t, where t is measured in decades after 1900. A colleague claims: "Because the model includes positive terms, the growth rate must eventually become positive for large values of t." Which of the following best evaluates this claim?