7
QuizMultiple Choice

Limits, Asymptotes, and End Behavior — Quiz

Question 7 • Precalculus

For function limit x to c raised to the negative power of h times x is equal to negative infinity and limit x to c raised to the plus power of h times x is equal to infinity Which statement describes the existence of an asymptote at c ?

Answer
A
There must be a horizontal asymptote at y is equal to c .
B
There is no asymptote at c because the one-sided limits are not equivalent.
C
There must be a vertical asymptote at x is equal to c .
D
There is no asymptote at c because the one-sided limits do not exist.

Explanation

A vertical asymptote occurs at x = c when the function’s values grow without bound as x approaches c from at least one side. Here, the left-hand limit is negative infinity and the right-hand limit is positive infinity, so x = c is a vertical asymptote. The one-sided limits do not need to be equal.

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