For what numbers x, - 2π≤ x ≤ 2π, does the graph of y = tan x have vertical asymptotes.?

{-3π/2, - π/2, π/2, 3π/2}

Step-by-step explanation:

The basic graph of the function y = tan x on - π/2 ≤ x ≤ π/2 is constrained by the asymptotes x = - π/2 (on the left) and x = π/2 (on the right. The period of the tangent function is π, so the first vertical asymptote to the left of x = - π/2 is x = - 3π/2 and the first to the right of x = π/2 is 3π/2.

In summary, the vertical asymptotes of y = tan x between - 2π ≤ x ≤ 2π are {-3π/2, - π/2, π/2, 3π/2}