00:01
For this problem, we are asked to find the vertical asymptotes of the graph of the function f of x equals secant x.
00:06
And then for part b, we're asked to describe the behavior of the function to the left and to the right of each vertical asymptote.
00:12
So the first thing that we can note here is that secant x is the same thing as 1 over cos of x.
00:19
So fx equals 1 over cos of x, which means that we'll have vertical asymptotes at all x such that cos of x equals 0.
00:28
Coase of x equals 0 for x or excuse me, cost of x is equal to 0 for any x, which is a odd multiple of pi by 2.
00:39
So we can say that they'll be found at n plus 1 pi by 2, where n is any integer.
00:46
So that gives us our list of all possible vertical asymptotes there.
00:56
Then from that, what we can do to describe the behavior to the last, left and to the right as requested in part b, can consider that around zero will be going off, starting at 1 and then going off towards positive infinity as we approach pi by 2.
01:20
And then as we go to the right from pi by 2, we'll be coming in from negative infinity, then returning to negative infinity...