Question

How do you graph `3sec(3x)`?

Answer 1

See graph and details.

Explanation:

`y = 3 sec ( 3 x ) = 3 / cos ( 3 x ) notin 3 ( - 1, 1 ) = ( - 3, 3 )`

Period = period of `cos ( 3 x ) = ( 2 pi ) / 3`

Asynptotes`x =` zeros of the denominator `cos ( 3 x )`.

`= ( 2 k + 1 )(pi/6) , k = 0, +-1, +-2, +-3, ...`

See Graph.
graph{(y cos (3x ) - 3)(y^2-9) = 0[-20 20 -10 10]}
Graph for one period `(2pi)/3, x in [ - pi/3, pi/3 ]`, sans asymptotic

`x = +- 1/6pi`:
graph{(y cos (3x ) - 3)(y^2-9)(x-1.04+0.001y) (x+1.04+0.001y)(x-0.52+0.001y) (x+0.52+0.001y)= 0[-3 3 -6 6 ]}