Question

Which of the following are vertical asymptotes of the function y = 3 cos (1/2x) - 4?

check all that apply.
a. x = π/2
b. x = 3 π
c. x = -2 π
d. x = 0

Answer 1

The vertical asymptotes of the function y = 3 cos (1/2x) - 4 are x = 0 and x = 2π.

Step-by-step explanation:

The vertical asymptotes of a function occur where the function approaches infinity or negative infinity as the input approaches a certain value. In the function y = 3 cos (1/2x) - 4, the vertical asymptotes can be found by solving for x when the cosine function equals 1 or -1.

Let's solve for x when cos (1/2x) = 1:

1 = cos (1/2x)

1/2x = 0

x = 0

So, one of the vertical asymptotes is x = 0.

Now, let's solve for x when cos (1/2x) = -1:

-1 = cos (1/2x)

1/2x = π

x = 2π

So, the other vertical asymptote is x = 2π.