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AP Calculus BC 1.14 Asymptotes Overview

Interpret one-sided infinite limits, vertical asymptotes and end behavior from graphs and limit statements, distinguishing local divergence from long-run horizontal behavior.

Syllabus
Effective Fall 2025
Course
AP Calculus BC

Exam points

  • connect derivative evidence to function behavior and interpretation
  • justify a calculus conclusion from symbolic, graphical or contextual evidence

Covered syllabus points

LIM-2.D—Interpret the behavior of functions using limits involving infinity

1.14 Connecting Infinite Limits and Vertical Asymptotes question 1

[Maximum number: 1]

The function f has the property that lim⁡x→1−f(x)=+∞,lim⁡x→1+f(x)=−∞,lim⁡x→−∞f(x)=2\lim _{x \rightarrow 1^{-}} f(x)=+\infty, \lim _{x \rightarrow 1^{+}} f(x)=-\infty, \lim _{x \rightarrow-\infty} f(x)=2, and lim⁡x→+∞f(x)=2\lim _{x \rightarrow+\infty} f(x)=2. Of the following, which could be the graph of f ?

A
Figure for Question 1.14 Connecting Infinite Limits and Vertical Asymptotes question 1 — AP Calculus BC — Option A
B
Figure for Question 1.14 Connecting Infinite Limits and Vertical Asymptotes question 1 — AP Calculus BC — Option B
C
Figure for Question 1.14 Connecting Infinite Limits and Vertical Asymptotes question 1 — AP Calculus BC — Option C
D
Figure for Question 1.14 Connecting Infinite Limits and Vertical Asymptotes question 1 — AP Calculus BC — Option D
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