Question

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

Answer 1

@nincompoop

Answer 2

@Nnesha

Answer 3

What are those things supposed to be 'included' in? A graph or a verbal explanation?

Answer 4

like written down

Answer 5

Okay. Knowing what sec is (1/cos, in case you forgot), what is the possible domain, just around 0, for this function? if cos(x) is equal to 0, there's no value for the function sec(x) because you can't divide by 0. That's where asymptotes form.

Answer 6

so the domain would be: all real numbers except π/4 + πn ?

Answer 7

no

Answer 8

but close
cosine is zero at \(\frac{\pi}{2}\) not \(\frac{\pi}{4}\)

Answer 9

If you want, @satellite73 , you can take over.

Answer 10

so what ould it be @satellite73
and thanks for your help @cathyangs

Answer 11

Or not? @pgreene008 you may be stuck with me XD.

So we've got the domain, and thus also know where asymptotes form. The period asks the length of the x-axis segments before the function repeats. You can find this by graphing or by using the equation breakdown of this struture ( https://mathway.com/examples/Trigonometry/Graphing-Trigonometric-Functions/Amplitude-Period-and-Phase-Shift?id=342) whichever style works for you.
Finally, the amplitude can be found either way above, as well.

Let me know if this all makes sense!

Answer 12

If you use Desmos you'll get all the info you require

Answer 13

so would this be the domain:??
Domain: all real numbers other than: ±π/4, ±3π/4, ±5π/4
@alekos @cathyangs

Answer 14

Yes, that's the domain

Answer 15

and so on i.e. ±(2n-1)π/4 where n = 1,2,3..........

Answer 16

so what would the final answer be?

Answer 17

Domain is all real numbers except x = ±(2n-1)π/4 where n = 1,2,3..........

Answer 18

The function is undefined at these points

Answer 19

A plot is attached.