HUNTERTUTORING
← AP
Get startedBook tutoring

Exam Strategy

Open PDF

Pre-calculus · AP · Polynomial and Rational Functions

CED focus

Rational Functions and Vertical Asymptotes

This topic is assessed on the AP Exam.

Multiple-choice tips

  • Ask whether the limit is one-sided, two-sided, or DNE before computing.
  • Factor or rewrite before choosing a limit or asymptote answer.
  • Eliminate MC choices that ignore holes vs vertical asymptotes.
  • Check end behavior signs from leading terms, not only a calculator window.
  • On rational items, test whether cancellation changes the graph (removable discontinuity).

Free-response tips

  • Use ‘approaches’ language; cite IVT or continuity when justifying.
  • State domain restrictions and asymptote locations before graphing.
  • Show factoring or long division that reveals holes and end behavior.
  • Label intercepts and asymptotes on a sketch; connect to the equation.
  • Interpret zeros and asymptotes in context when the stem is applied.

Common traps

  • Equating lim f(x) as x→a with f(a) when a hole exists
  • Treating every canceled factor as an asymptote instead of a hole
  • Confusing far-left/far-right behavior with local max/min
  • Using a calculator graph without stating algebraic end behavior

Quick checklist

  • [ ] Can state domain and asymptote locations for one rational example
  • [ ] Can factor or divide to expose a hole
  • [ ] Can explain end behavior from leading terms

For your personal study only. Copying, printing, screenshotting, or sharing this material is not permitted and may result in loss of access.

Back to 1.9