Final answer:
One vertical asymptote of the function y = tan(1/2)x + 2 is at x = 2π. The +2 vertical shift does not change the position of the asymptotes.
Step-by-step explanation:
One asymptote of the function tan(1/2)x+2 can be found by looking at the behavior of the tangent function. The tangent function has vertical asymptotes wherever the cosine function is zero since the tangent is the ratio of sine to cosine (tan(x) = sin(x)/cos(x)). For the function tan(1/2)x, the asymptotes occur at values of x where (1/2)x is an odd multiple of π/2, such as π, 3π/2, 2π, and so on. Because we are interested in tan(1/2)x, we need to double these values, resulting in asymptotes at x = 2π, x = 3π, x = 4π, etc. The vertical shift of +2 does not affect the x-coordinates of the asymptotes, so one of the vertical asymptotes of the function y = tan(1/2)x + 2 is x = 2π.