Which of the following is an asymptote of y = sec(x)? a. x=-2pi b. x=-pi/6 c. x=pi d. x=3pi/2

option d. x = 3π/2

Solution:

function y = sec(x)

1) y = 1 / cos(x)

2) When cos(x) = 0, 1 / cos(x) is not defined

3) cos(x) = 0 when x = π/2, 3π/2, 5π/2, 7π/2, ...

4) limit of sec(x) = lim of 1 / cos(x).

When x approaches π/2, 3π/2, 5π/2, 7π/2, ... the limit →+/- ∞.

So, x = π/2, x = 3π/2, x = 5π/2, ... are vertical asymptotes of sec(x).

3π/2

The figures attached will help you to understand the graph and the existence of multiple asymptotes for y = sec(x).