Which function does not have an asymptote?

Question

(1 point)
Responses

y = sec x
y = sec x

y = cot x
y = cot x

y = csc x
y = csc x

y = cos x

Answer 1

Among the given functions, \( y = \cos x \) does not have any asymptotes.

The functions \( y = \sec x \), \( y = \cot x \), and \( y = \csc x \) all have vertical asymptotes due to their definitions:

• \( y = \sec x \) has asymptotes where \( \cos x = 0 \).
• \( y = \cot x \) has asymptotes where \( \sin x = 0 \).
• \( y = \csc x \) has asymptotes where \( \sin x = 0 \).

In contrast, \( y = \cos x \) is a continuous function that oscillates between -1 and 1 and does not have any asymptotes.