Question

Analyze the function f(x) = sec 2x. Include: - Domain and range - Period and Amplitude - Two Vertical Asymptotes

Answer 1

i'd graph the curve 1st makes it easier to look at domain, range etc

Answer 2

Asec(b + cx). The period of the function is the normal period of secant, which is 2pi, divided by c. So 2pi/2 = pi, so you're period is pi. Now siince we have no b term, we do not have to worry about any shift left and right in the graph, it's positioned like normal. Next, the amplitude is just normal because the A term is simply 1. So this is a normal secant graph with no changes other than the fact that the period is pi instead of 2pi.

Any idea about how the graph of secant looks normally without the 2x?

Answer 3

would the answer be Range:(-∞,-1) U (1,∞)
Period: π
Asymptotes:x=±π/4, x=±3π/4, x=±5π/4
Domain: all real numbers other than: ±π/4, ±3π/4, ±5π/4

Answer 4

here is a graph good and read the comments posted and look at the graph