Question

What is the period and asymptote in y= tan(2x-pi)

Answer 1

for y = tan kØ , the period of the tangent curve is π/k
(notice that this differs from the period definition for sine and cosine)

so the period of tan (2x-π) is π/2 radians or 90°

We know that tan (π/2) is undefined (a vertical asymptote)
so 2x - π = π/2
2x = 3π/2
x = 3π/4

So your function will have a vertical asymptote at
x = 3π/4 , and one every π/2 to the right or to the left after that

vertical asymptotes:
in radians : x = 3π/4 + kπ/2 , where k is an integer
in degrees : x = 135° + 90k° , where k is an integer