y = - 2 sec ( x - pi )

Formula: sec x = 1/cos x
Then y = -2 sec ( x - pi ) = -2/cos ( x - pi )
Step 1:
Find those points where the value of y = - 2 sec ( x - pi ) = -2/cos ( x - pi ) is infinity.
The graph of y = cos(x) nd y = cos(x - pi).
when x = pi/2, cos ( x - pi ) = cos (pi/2 - pi) = cos (-pi/2) = cos (pi/2) = 0 ,
y = - 2 sec ( x - pi ) = -2/cos ( x - pi ) = -2/cos ( pi/2 - pi ) = -2/0 = infinity
when x = 3pi/2, cos ( x - pi ) = cos (3pi/2 - pi) = cos pi/2 = 0,
y = - 2 sec ( x - pi ) = -2/cos ( x - pi ) = -2/cos ( 3pi/2 - pi ) = -2/0 = infinity
Step 2:
Draw the graph y = - 2 sec ( x - pi ) = -2/cos ( x - pi )
draw the graph of y = y = - 2 sec ( x - pi )
Note:
1. The graph of y = cos(x - pi) is the graph of y = cos(x) right shift pi unit.
2. Since sec(x) = 1/cos(x), so when the value of cos(x) is zero, the value of sec(x) is infinity.