AP Calculus BC 1.14: Infinite Limits & Asymptotes

Practise AP Calculus BC 1.14 questions by matching one-sided and end-behaviour limits to graphs with vertical and horizontal asymptotes.

Exam points

Match one-sided infinite limits to a graph's vertical-asymptote behaviour near x-values.
Use end-behaviour limits to identify horizontal asymptotes and reject incompatible graphs.

[Maximum number: 1]

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

Figure for Question LIM-2.D—Interpret the behavior of functions using limits involving infinity question 1 — AP Calculus BC — Option A

Figure for Question LIM-2.D—Interpret the behavior of functions using limits involving infinity question 1 — AP Calculus BC — Option B

Figure for Question LIM-2.D—Interpret the behavior of functions using limits involving infinity question 1 — AP Calculus BC — Option C

Figure for Question LIM-2.D—Interpret the behavior of functions using limits involving infinity question 1 — AP Calculus BC — Option D

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LIM-2.D—Interpret the behavior of functions using limits involving infinity question 1