N/A — Exam

Question 23 • Precalculus

For function f of x , which pair of limits would verify the existence of a vertical asymptote at x is equal to negative 1 ?

Answer

limit x to negative infinity of f times x is equal to negative 1 and limit x to infinity of f times x is equal to negative 1

limit x to c raised to the negative power of f times x is equal to negative 1 and limit x to c raised to the plus power of f times x is equal to negative 1 for some value c

limit x to negative 1 raised to the negative power of f times x is equal to c and limit x to negative 1 raised to the plus power of f times x is equal to c for some value c

limit x to negative 1 raised to the negative power of f times x is equal to infinity and limit x to negative 1 raised to the plus power of f times x is equal to infinity

Explanation

A vertical asymptote at x = −1 occurs when f(x) grows without bound as x approaches −1 from at least one side. Choice D gives infinite limits from both the left and the right, so it verifies a vertical asymptote at x = −1. Choice C has finite limits, which would not indicate a vertical asymptote.

AI-written and checked against the verified answer.

More from this Course

Exam

Practice Exam

Practice Exam