AP Precalculus – Equivalent Representations – Drill 1

About This Drill

AP Precalculus – Equivalent Representations – Drill 1 is a Math practice drill covering Equivalent Representations. 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 equivalent representations of rational expressions (Topic 1.11). Practice rewriting expressions through factoring, polynomial long division, and simplification — and learn to choose the form that best reveals a specific feature of a function, such as its zeros, end behavior, or removable discontinuities.

Questions in This Drill

1. Which of the following is equivalent to \( \dfrac{x^2 + 3x - 10}{x - 2} \) for all x ≠ 2?
2. Using polynomial long division, which of the following is equivalent to \( \dfrac{2x^3 - x^2 + 4x - 3}{x - 1} \)?
3. A company's total production cost (in dollars) is modeled by C(x) = 3x + 500, where x is the number of units produced (x > 0). The average cost per unit is \( A(x) = \dfrac{3x + 500}{x} \). Which equivalent form of A(x) best reveals the long-run average cost behavior as production increases without bound?
4. Which of the following is an equivalent form of \( f(x) = \dfrac{x^2 - 4}{x + 2} \) that reveals a feature not visible in the original expression?
5. A student rewrites \( g(x) = \dfrac{x^3 + 8}{x + 2} \) using polynomial long division and obtains \( g(x) = x^2 - 2x + 4 \) for all real x. A second student says this rewrite is incorrect because the original function is undefined at x = −2. Which of the following best evaluates the second student's claim?