Secant is the reciprocal of cosine, sec=1/cos(x).Only thing is when x equals 0 for cosine the reciprocal does not resist. The first picture shows to periods of pi. The range is infinity to -1 and 1 to infinity. The second picture shows the amplitude, Y=2sec(x) the range 2 - infinity. It only has an height. The next picture is the period shift and that has a range of 1 to infinity or -1 to infinity. It has only period in this picture. Y=sec(2x) had the period shift as 2. The 4th picture is Y=sec(x-2) which shows the horizontal shift and that has the same range besides it moves it to left two times. The last picture is Y=2+sec(x), showing the vertical shift as 2. The vertical shift is just alternating the height. The range does not change although it make look like it, it just move the x-axis higher or lower depending on the sign +/-. This is the way i like to think of it.