Step-by-step explanation:
sec(x) = 1/cos(x)
and therefore, it behaves accordingly.
the minimum of cos(x) is the maximum of 1/cos(x).
it does not have any x-intercepts. for cos(x) = 1 (max) we get 1/1 = 1 for sec(x), which is the minimum.
mirrored to this, cos(x) = -1 gives us also -1 for sec(x).
sec(x) = 1/cos(x) can never have a result between -1 and +1.
cos(0) = 1, so also sec(x) = 1, and therefore (0, 1) is the y-axis intercept.
at every pi (beginning at 0) there is a horizontal tangent, but not an asymptote. the (vertical) asymptotes happen at every pi beginning at pi/2 and -pi/2.
therefore, only the third and fourth answer options are correct.
