Question

Locate the vertical asymptotes, and sketch the graph of y = sec (x - π) + 3.

Answer 1

Since secant is the inverse of cosine function, when the cosine function has a 'zero' the secant will have a vertical asymptote.

Graphing a cosine with a right shift of pi, the zeros would be at pi and 2pi.
This will make the vertical asymptotes of the secant function be at pi and 2pi.

I hope you understand.