Question 1203784
euation is f(x) = 5sec(3x)
general form is f(x) = a * sec(b * (x-c)) + d
a is the amplitude.
b is the frequency.
c is the horizontal shift.
d is the vertical shift.


i believe they are referring to the amplitude as the stretching factor.
the default is 1 unit above and 1 unit below the center horizontal line.
when it is 5, the amplitude is 5 times as much above and below the horizontal line.


the normal period of the secant function is 360 degrees.
the freuency for the secant function is equal to 360 / the period.
the period for the secant function is equal to 360 / the frequency.
the frequency for this secant function is 3.
the period is therefore 360 / 3 = 120 degrees.


there is no horizontal shift.
here is no vertical shift.


the graph of this runction is shown below.


<img src = "http://theo.x10hosting.com/2023/092103.jpg">


the secant function is in red.
the cosine function is in blue.


you want the secant function.
i only showed the cosine function because the secant function is equal to 1 divided by the cosine function.
i thought it would be easier for you to see that it is the reciprocal of the cosine function that way.
the graph that you want is the red graph.


the asymptotes are at 0 degrees and at 120 degrees.
that's where the cosine function = 0.
since the secant function is 1 / cosine function, that's where the secant function is undefined.