Question

How do you graph `y=-2sec(1/2x)`?

Answer 1

See explanation and graph.

Explanation:

sec values `notin ( - 1, 1 )`

`y = - 2 sec ( 1/2 x ) notin ( -2, 2 ) and x ne` asymptotic (2k+1)pi#,

`k = 0, +-1,+-2, +-3, ...`

The period is the period `(2pi)/(1/2) = 4pi` of #cos ( 1/2 x ).

See graph depicting all these aspects.
graph{(ycos(x/2) +2)(y-2+0x)(y+2+0x)(x+pi+0.0001y)(x-3pi+0.0001y)(x+3pi+0.0001y)(x-pi+0.0001y)=0[-20 20 -10 10]} .